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ΑΡΙΘΜΟΙ 6001 - 7000

6001 has a cube that is a concatenation of other cubes.
6002 is the number of digits of the 24^th Mersenne prime.
6003 has a square with the first 3 digits the same as the next 3 digits.
6006 is the number of intersections when all the diagonals of a regular 21-gon are drawn.
6008 = ₁₄C₆ + ₁₄C₀ + ₁₄C₀ + ₁₄C₈.
6009 is a strobogrammatic number.
6011 is a member of the Fibonacci-type sequence starting with 3 and 8.
6012 has a square with the last 3 digits the same as the 3 digits before that.
6014 has a square that is formed by 3 squares that overlap by 1 digit.
6016 is the maximum number of pieces a torus can be cut into with 32 cuts.
6017 is a centered octahedral number.
6018 is the maximum number of regions a cube can be cut into with 33 cuts.
6020 is the number of Hamiltonian graphs with 8 vertices.
6021 has a square that is formed by 3 squares that overlap by 1 digit.
6024 is a value of n for which |cos(n)| is smaller than any previous integer.
6025 are the last 4 digits of the sum of the first 6025 squares.
6032 is the number of ways to place 2 non-attacking knights on a 9×9 chessboard.
 6035 is a number whose sum of divisors is a 5^th power.
6040 is the number of ways to divide 6 couples into pairs where no pair is a couple.
6048 is the order of a non-cyclic simple group.
6050 has a sum of digits equal to its largest prime factor.
6058 is a number that does not have any digits in common with its cube.
6065 is the closest integer to 16^π.

6070 is a structured truncated tetrahedral number.

6072 is the order of a non-cyclic simple group.

6073 is the order of a non-cyclic simple group.

6075 is an Achilles number.

6077 has a square with the last 3 digits the same as the 3 digits before that.

6080 is the smallest number n>1 whose base 14 representation is equal to φ(n).

6081 has a cube that is the sum of 3 positive cubes.

6083 has a square that is the sum of a cube and a 4^th power.

6084 is the sum of the first 12 cubes.

6092 is the number of 16-ominoes with a line of symmetry.

6093 is a value of n for which 3n and 5n together use each digit exactly once.

6095 is a rhombic dodecahedral number.

6097 is an hexagonal prism number.

6099 concatenated with its successor is square.

6100 has the property that if each digit is replaced by its square, the resulting number is a square.

6102 is the largest number n known where φ(n) is the reverse of n.

6105 is a Huay rhombic dodecahedral number.

6106 is a value of n for which 2φ(n) = φ(n+1).

6107 is a Perrin number.

6111 is a value of n for which σ(n-1) = σ(n+1).

6119 is a strobogrammatic number.

6120 is a highly abundant number.

6121 is the smallest number whose cube contains 4 consecutive 3's.

6128 is a betrothed number.

6137 is a centered dodecahedral number.

6138 is the number of quasi-tetrominoes that fit inside a 7×7 grid.

6141 is a Kaprekar constant in base 2.

6142 is the number of inequivalent asymmetric Ferrers graphs with 34 points.

6143 is the smallest prime that contains twelve 1's in binary.

6144 = 16!!!!.

6145 is a Friedman number.

6153 is the number of partitions of 40 that do not contain 1 as a part.

6155 is a member of the Fibonacci-type sequence starting with 2 and 5.

6164 is the number of 11-ominoes that tile the plane using 180 degree rotations.

6167 has a 4^th power that is the sum of four 4^th powers.

6168 is the number of inequivalent Ferrers graphs with 34 points.

6170 = 5 + 55 + 555 + 5555.

6171 has the property that dropping its first and last digits gives its largest prime factor.

6173 is a prime that remains prime if any digit is deleted.

6174 is the Kaprekar constant for 4-digit numbers.

6175 is the number of regions formed when all diagonals are drawn in a regular 21-gon.

6176 is the last 4-digit sequence to appear in the decimal expansion of π.

6179 is a value of n for which 4n and 5n together use each digit exactly once.

6180 is the smallest number n with φ(n) = 2 reverse(n).

6181 is an octahedral number.

6187 is a Smith brother.

6188 = ₁₇C₅.

6189 is the number of ways to write 17 as an ordered sum of positive integers, where adjacent numbers are different.

6194 is the number of ways to place a non-attacking white and black pawn on a 10×10 chessboard.

6196 is the number of regions the complex plane is cut into by drawing lines between all pairs of 21^st roots of unity.

6197 is a narcissistic number in base 6.

6200 is a harmonic divisor number.

6201 is the sum of the first 26 squares.

6210 is the number of 5×5 matrices with non-negative entries with every row and column adding to 2.

6211 is a Cuban prime.

6216 has a square with the first 3 digits the same as the next 3 digits.

6219 is a value of n for which 4n and 5n together use each digit exactly once.

6220 = 44444 in base 6.

6221 = 666 + 2222 + 2222 + 1111.

6222 is the smallest number that can not be written as the sum of 2 triangular numbers and a power of 2.

6223 = 666 + 2222 + 2 + 3333.

6224 is the number of permutations of 8 elements that have 4^th power equal to the identity permutation.

6225 = 666 + 2 + 2 + 5555.

6232 is an amicable number.

6235 is the number of different resistances that can be formed by eleven or fewer 1-ohm resistors in series or parallel.

6237 is a number whose sum of the squares of its divisors is a square.

6239, followed by 6239 7's, is prime.

6240 is a highly abundant number.

6244 is a member of the Fibonacci-type sequence starting with 2 and 9.

6245 is the smallest number whose square contains 4 consecutive internal 0's.

6248 is the smallest number with the property that its first 8 multiples contain the digit 4.

6249 is the smallest number with the property that its first 10 multiples contain the digit 4.

6250 is a Leyland number.

6256 is a hendecagonal pyramidal number.

6257 is the number of essentially different ways to dissect a 20-gon into 9 quadrilaterals.

6266 is a truncated octahedral number.

6267 is the number of 15-iamonds with holes.

6270 is a value of n for which n-1 and n+1 are twin primes, and so are 2n-1 and 2n+1.

6271 is the smallest number requiring an addition chain of length 17.

6272 is the number of ways to tile a 4×29 rectangle with 4×1 rectangles.

6273 is the number of ways to 9-color the vertices of a pentagon, up to rotations and reflections.

6274 has a cube whose digits occur with the same frequency.

6276 is a value of n for which φ(n) = φ(reverse(n)).

6279 is the number of subsequences of {1,2,3,...14} in which every odd number has an even neighbor.

6280 has a sum of prime factors that is equal to the sum of the prime factors of the two preceding numbers.

6290 is the number of 13-iamonds that do not tile the plane.

6293 is the number of ordered partitions of 24 into distinct parts.

6296 has a square with the first 3 digits the same as the next 3 digits.

6297 is a value of n for which n and 5n together use each digit 1-9 exactly once.

6299 is the smallest number with complexity 30.

6300 is divisible by its reverse.

6307 is the largest n so that Q(√n) has class number 8.

6309 is the closest integer to 25^e.

6310 is the smallest number whose 5^th power has 19 digits.

6312 is the sum of its proper divisors that contain the digit 5.

6318 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

6320 is the Entringer number E(8,4).

6322 is the number of idempotent functions from a set of 7 elements into itself.

6327 = 324 + 325 + . . . + 342 = 343 + 344 + . . . + 360.

6331 has the same digits as the 6331^st prime.

6332 is the number of fullerenes with 68 carbon atoms.

6336 is the number of ways to tile a 9×4 rectangle with 2×1 rectangles.

6343 is the number of quasi-triominoes that fit inside a 14×14 grid.

6347 has the same digits as the 6347^th prime.

6348 is a pentagonal pyramidal number.

6351 is the largest number known that is not the sum of 3 squares or cubes.

6354 is the number of 14-iamonds that tile the plane.

6360 is a value of n for which n-1 and n+1 are twin primes, and so are 3n-1 and 3n+1.

6368 is an amicable number.

6371 has a square that is the sum of 2 relatively prime cubes.

6374 is a value of n for which 4n and 5n together use each digit exactly once.

6375 has a square with the first 3 digits the same as the next 3 digits.

6378 is the number of partitions of 55 into distinct parts.

6379 is a value of n for which |cos(n)| is smaller than any previous integer.

6380 is a value of n for which n! + 1 is prime.

6381 is the smallest value of n for which n and 9n together use each digit 1-9 exactly once.

6384 is an icosahedral number.

6385 is the number of ways to stack 18 pennies in a line so that each penny lies on the table or on two pennies.

6389 is the number of functional graphs on 11 vertices.

6391 is a hexagonal pyramidal number.

6395 is the number of ways to divide a 12×12 grid of points into two sets using a straight line.

6396 is a divisor of the sum of the 4^th powers of its divisors.

6397 has the same digits as the 6397^th prime.

6399 and its successor are both divisible by 4^th powers.

6400 is a square whose digits are non-increasing.

6403 has a square with the first 3 digits the same as the last 3 digits.

6404 is a value of n for which n!! - 1 is prime.

6406 is the number of permutations of 8 elements where every cycle has equal length.

6408 is the sum of the squares. of the first 13 primes.

6409 is a house number.

6411 is a truncated cube number.

6424 is the number of minimal covers of a set containing 6 elements.

6427 is the number of ways a 6×6 square can be tiled with 1×1 and 2×2 squares.

6432 has the same digits as the 6432^nd prime.

6434 is the number of divisors of the 18^th perfect number.

6435 = ₁₅C₇.

6440 is a value of n for which n!!!! + 1 is prime.

6443 has a cube whose digits occur with the same frequency.

6444 is the smallest number whose 5^th power starts with 5 identical digits.

6445, followed by 6445 1's, is prime.

6454 is the smallest value of n for which π(10n) = n.

6455 is the smallest value of n for which the n^th prime begins with the digits of n.

6456 is a value of n for which the n^th prime begins with the digits of n.

6457 is a value of n for which the n^th prime begins with the digits of n.

6458 would be prime if preceded and followed by a 1, 3, 7, or 9.

6459 is a value of n for which the n^th prime begins with the digits of n.

6460 is a value of n for which the n^th prime begins with the digits of n.

6462 divides the sum of the digits of 6462!.

6466 is the largest known value of n for which the n^th prime begins with the digits of n.

6471 is a value of n for which n and 9n together use each digit 1-9 exactly once.

6472 is the number of polyominoes with 9 or fewer squares.

6475 is a value of n for which π(n) is the product of the digits of n.

6479 is a value of n for which n and 8n together use each digit 1-9 exactly once.

6481 = (3¹² + 1) / (3⁴ + 1).

6487 is the number of partitions of 51 in which no part occurs only once.

6488 would be prime if preceded and followed by a 1, 3, 7, or 9.

6489 is half again as large as the sum of its proper divisors.

6490 is the number of ways to place 2 non-attacking bishops on a 11×11 chessboard.

6498 is the index of a triangular number containing only 3 different digits.

6500 is a number n whose sum of the factorials of its digits is equal to π(n).

6501 has a square whose reverse is also a square.

6505 is the number of 9-hexes without holes.

6506 is a value of n for which the first n binary digits of π form a prime.

6510 is a number n whose sum of the factorials of its digits is equal to π(n).

6511 is a number n whose sum of the factorials of its digits is equal to π(n).

6512 is the number of 11-ominoes that tile the plane isohedrally.

6514 is the sum of the 4^th powers of the digits of the sum of the 4^th powers of the digits of itself.

6517 has a sum of digits equal to its largest prime factor.

6521 is a number n whose sum of the factorials of its digits is equal to π(n).

6523 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

6524 has the property that its square starts with its reverse.

6525 is a centered icosahedral number.

6526 is the smallest number whose 10^th power contains exactly the same digits as another 10^th power.

6527 is a value of n for which φ(n) = φ(n-1) + φ(n-2).

6529 is a Proth prime.

6532 is a member of the Fibonacci-type sequence starting with 1 and 6.

6533 is the number of digits of the 25^th Mersenne prime.

6534 is a value of n for which 3n and 7n together use each digit exactly once.

6537 is the smallest value of n for which the numbers n-6 through n+6 can not be written as the sum of 2 squares.

6540 is the number of terms in the 17^th derivative of f(f(f(x))).

6543 has a square root that has four 8's immediately after the decimal point.

6544 is a number n whose 9^th root has a decimal part that begins with the digits of n.

6545 and its reverse are tetrahedral numbers.

6547 is the number of binary 4×4 matrices with no row or column containing 3 consecutive 1's.

6552 is the number of different full houses in 5 card poker with one joker.

6553 is a Lucas 5-step number.

6556 is the largest palindrome that can be made using 5 digits and the 4 arithmetic operations.

6557 is the product of two consecutive primes.

6560 is the smallest number n where n and n+1 are both products of 7 or more primes.

6561 = 3⁸.

6569 is a value of n for which one less than the product of the first n primes is prime.

6572 is the number of 9-hexes.

6576 = (6! - 6) + (5! - 5) + (7! - 7) + (6! - 6).

6578 is the smallest number which can be written as the sum of three 4^th powers in 2 ways.

6579 is the number of ways to color the vertices of a triangle with 27 colors, up to rotation.

6580 is the maximum number of regions a cube can be cut into with 34 cuts.

6581 has the same digits as the 6581^st prime.

6583 is a value of n for which σ(φ(n)) = 2σ(n).

6586 is a value of n for which n!!!! + 1 is prime.

6588 is the number of sided 12-iamonds.

6593 = 6 + 5555 + 999 + 33.

6594 is a value of n for which 5n and 7n together use each digit exactly once.

6596 has a square comprised of the digits 0-7.

6601 is a Carmichael number.

6603 is a number whose square and cube use different digits.

6608 is the maximum number of regions space can be divided into by 28 spheres.

6609 has a 4^th power that is the sum of four 4^th powers.

6611 is a value of n such that the n^th Cullen number is prime.

6615 is an odd abundant number.

6620 is the number of 11-ominoes that tile the plane.

6623 has the property that the sum of its prime factors is equal to the product of its digits.

6630 is the number of triangles of any size contained in the triangle of side 29 on a triangular grid.

6636 has exactly the same digits in 3 different bases.

6639 divides 1¹ + 2² + 3³ + ^{. . .} + 6639⁶⁶³⁹.

6642 can be written as the sum of 2 or 4 positive 4^th powers.

6643 is the smallest number which is palindromic in bases 2 and 3.

6647 has a sum of digits equal to its largest prime factor.

6651 is the index of a triangular number containing only 3 different digits.

6653, when concatenated with 4 less than itself, is square.

6654 is the smallest number whose decimal part of its 4^th root starts with the digits 0-9 in some order.

6663 is a value of n for which σ(n) is a repdigit.

6665 is a centered tetrahedral number.

6666 is a repdigit.

6667 is the number of self-dual planar graphs with 24 edges.

6668 is the number of trees on 21 vertices with diameter 5.

6669 is the sum of 3 consecutive cubes.

6680 = 6666 + 6 + 8 + 0.

6681 = 6666 + 6 + 8 + 1.

6682 = 6666 + 6 + 8 + 2.

6683 = 6666 + 6 + 8 + 3.

6684 = 6666 + 6 + 8 + 4.

6685 = 6666 + 6 + 8 + 5.

6686 = 6666 + 6 + 8 + 6.

6687 = 6666 + 6 + 8 + 7.

6688 = 6666 + 6 + 8 + 8.

6689 = 6666 + 6 + 8 + 9.

6694 is a value of n for which the sum of the first n primes is square.

6699 is a strobogrammatic number.

6700 has a cube that contains the digits 6700 in reverse order.

6704 is the number of rooted 8-hexes.

6706 is the number of Hamiltonian paths in a 8×5 rectangle graph.

6712 is the index of a triangular number containing only 3 different digits.

6714 is the index of a triangular number containing only 3 different digits.

6716 is the 4-digit string that appears latest in the decimal expansion of π.

6720 = ₈P₅.

6721 is a composite value of n that divides the (n-1)^st Fibonacci number.

6723 is a value of n for which 3n and 8n together use each digit exactly once.

6726 is the 10^th Pell-Lucas number.

6728 is the number of domino tilings of a 6×6 square.

6729 is the smallest value of n for which n and 2n together use each digit 1-9 exactly once.

6731 would be prime if preceded and followed by a 1, 3, 7, or 9.

6732 is a value of n for which _2nC_n is divisible by n².

6734 is a value of n for which |cos(n)| is smaller than any previous integer.

6735 is a stella octangula number.

6736 is the number of 3×3 sliding puzzle positions that require exactly 17 moves to solve starting with the hole in the center.

6740 is the number of 13-iamonds that do not tile the plane.

6741 is a value of n for which n and 8n together use each digit 1-9 exactly once.

6742 has a square where the first 6 digits alternate.

6743 is the number of binary 4×5 matrices with no consecutive 1's in any row or column.

6745 is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 25 stamps.

6751 is the number of digits of the 23^rd perfect number.

6754 is the smallest number in base 9 to have 5 different digits.

6756 has a cube that is the sum of 3 positive cubes.

6757 is the number of connected graphs with 10 vertices and 34 edges.

6759 is the number of graphs with 10 vertices and 11 edges.

6764 is the sum of the first 18 Fibonacci numbers.

6765 is the 20^th Fibonacci number.

6768 has a 9^th root that starts 2.664444666....

6769 is the Stirling number of the first kind s(8,4).

6772 has a square whose digits each occur twice.

6779 = 6666 + 7 + 7 + 99.

6780 has the same digits as the 6780^th prime.

6786 is a triangular number whose internal digits are triangular and whose external digits are triangular.

6788 is the smallest number with multiplicative persistence 6.

6789 is the largest 4-digit number with increasing digits.

6791 is a value of n for which n and 8n together use each digit 1-9 exactly once.

6792 is a value of n for which n and 2n together use each digit 1-9 exactly once.

6793 is the smallest prime so that it and the next 2 primes all end in 3.

6794 has the property that dropping its first and last digits gives its largest prime factor.

6797 is a number whose sum of divisors is a 5^th power.

6799 is the number of different degree sequences possible for a graph with 18 edges.

6801 has a 4^th power that is the sum of four 4^th powers.

6802 is the number of ways to move a rook from corner to opposite corner on a 6×6 chessboard.

6811 is not the sum of a square, a cube, a 4^th power, and a 5^th power.

6813 is the smallest number whose 6^th power has 24 digits.

6816 is the index of a triangular number containing only 3 different digits.

6818 = 1⁸ + 2⁸ + 3⁸.

6819 = 20457 / 3, and each digit is contained in the equation exactly once.

6820 is the number of regions formed when all diagonals are drawn in a regular 23-gon.

6822 uses the same digits as φ(6822).

6825 is an odd primitive abundant number.

6828 is the number of ways to start with a knight in the corner of an 8×8 chessboard, make 8 moves, and end on the same square.

6831 is a structured truncated octahedral number.

6837 is the number of 8-digit squares.

6839 is a value of n for which n and 8n together use each digit 1-9 exactly once.

6840 is the number of ways to place 2 non-attacking kings on a 11×11 chessboard.

6842 is the number of partitions of 31.

6845 would be prime if preceded and followed by a 1, 3, 7, or 9.

6849 is a value of n for which 2n and 3n together use each digit exactly once.

6850 is the smallest value of n for which n, n+1, n+2, n+3, n+4, and n+5 have the same number of prime factors.

6853 is a value of n for which n, n+1, n+2, and n+3 have the same number of divisors.

6859 = 19³.

6860 is a heptagonal pyramidal number.

6861 is a value of n for which σ(n-1) + σ(n+1) = σ(2n).

6863 is a prime that is the sum of the square of a prime and the cube of a prime.

6864 = 6666 + 88 + 66 + 44.

6865 is the maximum value of n so that there exist 5 denominations of stamps so that every postage from 1 to n can be paid for with at most 17 stamps.

6867 can be written as the sum of 2, 3, 4, or 5 positive cubes.

6868 is the larger number in a Ruth-Aaron pair.

6874 is equal to the sum of its anti-divisors.

6875 is 3-automorphic.

6879 is the number of planar partitions of 15.

6880 is a vampire number.

6886 is a palindrome in base 9 and in base 10.

6888 has a square with 3/4 of the digits are the same.

6889 is a strobogrammatic square.

6895 is a value of n for which 2n and 7n together use each digit exactly once.

6896 has a square root whose decimal part starts with the digits 0-9 in some order.

6900 is the number of ways to place 2 non-attacking knights on a 11×11 chessboard.

6902 is the number of Hamiltonian paths of a 3×10 rectangle graph.

6903 is a value of n for which σ(n-1) = σ(n+1).

6905 has a 5^th root whose decimal part starts with the digits 1-9 in some order.

6912 = 6 × 9 × 1 × 2⁷.

6917 is a value of n for which n! - 1 is prime.

6918 = 20754 / 3, and each digit is contained in the equation exactly once.

6919 is the number of non-invertible knots with 13 crossings.

6922 is the number of polycubes containing 8 cubes.

6924 is the magic constant of a 24×24 magic square.

6926 has a square whose digits each occur twice.

6927 is a value of n for which n and 2n together use each digit 1-9 exactly once.

6928 is the number of inequivalent binary linear codes of length 11.

6930 is the square root of a triangular number.

6931 has the same digits as the 6931^st prime.

6935 is the smallest number whose cube contains six 3's.

6936 is the number of ways to legally add 2 sets of parentheses to a product of 16 variables.

6939 is a value of n for which 3n and 5n together use each digit exactly once.

6940 is the sum of its proper divisors that contain the digit 3.

6941 has a square whose digits each occur twice.

6942 is the number of labeled topologies with 5 elements.

6944 is the number of degree sequences for graphs with 6 vertices.

6949 is the smallest number that can not be written as the sum of 3 volumes of rectangular boxes with integer dimensions less than 16.

6951 has exactly the same digits in 3 different bases.

6952 = 1738 × 4 and each digit from 1-9 is contained in the equation exactly once.

6953 = 66 + 999 + 5555 + 333.

6954 is the trinomial coefficient T(19,15).

6956 is the number of triangles formed by drawing all diagonals of a regular 12-gon.

6960 is the number of ways to place 2 non-attacking queens on a 10×10 chessboard.

6966 is the number of planar graphs with 8 vertices.

6969 is a strobogrammatic number.

6972 is the number of possible positions in Checkers containing 2 checkers.

6976 is the number of binary 5×5 matrices A with the property that A²=0 (mod 2).

6982 is a value of n for which the sum of the first n composite number numbers is a square.

6983 is the smallest prime that can only be made into 1 other prime by changing a single digit.

6984 can be written as the sum of 2, 3, 4, or 5 positive cubes.

6985 is the smallest number that can be written as the sum of 3 or more consecutive squares, or as the sum of 3 or more consecutive cubes.

6987 is the number of digits of the 26^th Mersenne prime.

6989 has the property that the concatenation of its prime factors in increasing order is a square.

6991 is a value of n for which reverse(φ(n)) = φ(reverse(n)).

6996 is a palindrome n so that n(n+8) is also palindromic.

6998 is a member of the Fibonacci-type sequence starting with 4 and 9.

6999 is the smallest number whose digits add to 33.

7000 has a sum of digits equal to its largest prime factor.