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ΑΡΙΘΜΟΙ 7001 - 8000

7001 is the number of 13-hexes that tile the plane by translation.
7002 is the number of arrangements of 4 non-attacking queens on a 8×8 chessboard.
7003 is the number of graphs with 9 vertices that have 8 automorphisms.
7014 has a square with the last 3 digits the same as the 3 digits before that.
7015 has a cube root whose decimal part starts with the digits 1-9 in some order.
7019 is a prime that remains prime if any digit is deleted.
7028 is the smallest multi-digit number n, when written in base 17, gives a divisor of n.
7030 is an octagonal pyramidal number.
7032 is the number of ternary square-free words of length 24.
7039 = 28156 / 4, and each digit is contained in the equation exactly once.
7040 has a sum of digits equal to its largest prime factor.
7055 is a Lucas-Carmichael number.
7056 is a square that is the product of two triangular numbers.
7057 is a Cuban prime.

7060 has the property that the sum of the squares of its divisors ends with the digits 7060.

7066 is the maximum value of n so that there exist 6 denominations of stamps so that every postage from 1 to n can be paid for with at most 13 stamps.

7068 is the number of series-reduced planted trees with 11 leaves.

7071 is the smallest number whose square contains 4 consecutive 9's.

7072 is the generalized Catalan number C(10,7).

7073 is a Leyland number.

7075 is the number of ways to stack 35 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

7084 is the generalized Catalan number C(19,4).

7089 is a value of n for which |cos(n)| is smaller than any previous integer.

7092 is the number of possible positions in Othello after 3 moves by both players.

7093 has a 6^th root that starts 4.38333833....

7094 is the number of ways to place 34 points on a 17×17 grid so that no 3 points are on a line.

7096 is the number of 8-digit perfect powers.

7098 is the trinomial coefficient T(14,9).

7101 has a 4^th power that is the sum of four 4^th powers.

7102 is the index of a Fibonacci number whose first 9 digits are the digits 1-9 rearranged.

7106 is an octahedral number.

7107 has a square whose digits each occur twice.

7108 is the number of partitions of 56 into distinct parts.

7117 is a number whose sum of divisors is a 5^th power.

7119 has the same digits as the 7119^th prime.

7120 is the number of 2×2 singular matrices mod 10.

7122 = 7² + 8³ + 9⁴.

7123 is the number of 2-connected graphs with 8 vertices.

7140 is the largest number which is both triangular and tetrahedral.

7142 is the smallest number that can not be written as the sum of 2 volumes of rectangular boxes with integer dimensions less than 20.

7143 is 7-automorphic.

7145 has a square with the first 3 digits the same as the next 3 digits.

7150 has a sum of digits equal to its largest prime factor.

7152 has a square with the first 3 digits the same as the next 3 digits.

7159 has a square with the first 3 digits the same as the next 3 digits.

7161 is a Kaprekar constant in base 2.

7164 is a value of n for which n⁸, n⁹, n¹⁰, and n¹¹ have the same digit sum.

7170 is a value of n for which σ(n-1) = σ(n+1).

7172 is a Kaprekar number for cubes.

7174 is the maximum number of pieces a torus can be cut into with 34 cuts.

7175 is a centered octahedral number.

7176 is the maximum number of regions a cube can be cut into with 35 cuts.

7187 is the smallest number that can not be formed using the digits 0-8 at most once, together with the symbols +, –, × and ÷.

7188 is the number of ways to permute 5 red, 5 white, and 5 blue balls.

7189 is the number of ways to color the vertices of a square with 13 colors, up to rotation.

7192 is a weird number.

7193 is a right-truncatable prime.

7197 is the smallest number whose 7^th power has 27 digits.

7200 is the order of a perfect group.

7201 is the number of 2×2 singular matrices mod 19.

7209 has a 4^th power that is the sum of four 4^th powers.

7212 is the number of unordered ways to write 1 as a sum of reciprocals of integers no larger than 20.

7225 is the number of ways to 17-color the faces of a tetrahedron.

7226 has a cube root that starts 19.3330030330....

7230 is the sum of consecutive squares in 2 ways.

7235 is a value of n for which 4n and 5n together use each digit exactly once.

7236 uses the same digits as φ(7236).

7240 = 1111 in base 19.

7241 is the number of asymmetric trees with 19 vertices.

7245 appears inside its 4^th power.

7248 is the number of lines through exactly 2 points of a 14×14 grid of points.

7253 has a square that remains square when a 6 is appended to it.

7254 = 186 × 39 and each digit is contained in the equation exactly once.

7256 is a value of n for which n, n+1, n+2, and n+3 have the same number of divisors.

7260 is a doubly triangular numbers.

7269 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7271 and its reverse are both differences of positive cubes.

7272 is a Kaprekar number.

7281 is a value of n for which 3n and 7n together use each digit exactly once.

7285 has a 7^th power that contains the same digits as 544¹⁰.

7286 is the number of subsets of {1,2,3,...,16} that have a sum divisible by 9.

7293 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7295 is a value of n for which 4n and 5n together use each digit exactly once.

7297 is a Proth prime.

7306 is the smallest number whose 7^th power starts with 7 identical digits.

7311 is the number of symmetric plane partitions of 33.

7312 is a value of n for which n and 8n together use each digit 1-9 exactly once.

7314 is the smallest number so that it and its successor are both products of 4 distinct primes.

7315 = ₂₂C₄.

7318 is the number of functions from 10 unlabeled points to themselves.

7320 is the number of triangles of any size contained in the triangle of side 30 on a triangular grid.

7321 is the number of intersections when all the diagonals of a regular 24-gon are drawn.

7322 is the number of 3×3 sliding puzzle positions that require exactly 17 moves to solve starting with the hole on a side.

7326 = 1 × 22 × 333.

7327 is a number whose sum of divisors is a 5^th power.

7329 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7330 is the number of unsymmetrical ways to dissect a regular 14-gon into 12 triangles.

7331 is a right-truncatable prime.

7333 is a right-truncatable prime.

7336 is the number of ways to color the vertices of a triangle with 28 colors, up to rotation.

7337 is a hexagonal pyramidal number.

7338 is the closest integer to 17^π.

7339 has a 4^th power that is the sum of four 4^th powers.

7341 has the same digits as the 7341^st prime.

7342 is the number of ways to stack 29 pennies in contiguous rows so that each penny lies on the table or on two pennies.

7344 is a value of n for which 4n and 7n together use each digit exactly once.

7345 has the same digits as the 7345^th prime.

7351 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

7353 is the largest number n known so that both n and n³ have only odd digits.

7356 is a value of n for which 5n and 7n together use each digit exactly once.

7358 is a composite number that remains composite when preceded or followed by any digit.

7359 is a Lucas 6-step number.

7360 can be written as the product of a number and its reverse in 2 different ways.

7361 is the number of ways to play the first 5 moves in Checkers.

7364 is a value of n for which n and 8n together use each digit 1-9 exactly once.

7366 is the maximum number of regions space can be divided into by 29 spheres.

7371 has a base 2 representation that begins with its base 9 representation.

7375 is a member of the Fibonacci-type sequence starting with 1 and 4.

7376 is a structured truncated tetrahedral number.

7380 is the number of numbers with 4 or fewer digits that do not contain any 0's.

7381 = 11111 in base 9.

7383 has a 4^th power that is 1/2 of the sum of three 4^th powers.

7384 has the same digits as the 7384^th prime.

7385 is a Keith number.

7387 is the product of two consecutive primes.

7393 is a right-truncatable prime.

7396 has a 4^th root whose decimal part starts with the digits 1-9 in some order.

7403 is the smallest number that can not be formed using the digit 1 at most 28 times, together with the symbols +, –, × and ÷.

7404 = 6 + 66 + 666 + 6666.

7410 = 361 + 362 + . . . + 380 = 381 + 382 + . . . + 399.

7413 is the number of even permutations on 8 elements with no fixed points.

7414 is a value of n for which φ(n) = φ(reverse(n)).

7416 is a value of n for which n and 8n together use each digit 1-9 exactly once.

7420 is the number of permutations of 8 items that fix 2 elements.

7421 is a value of n for which 4n and 5n together use each digit exactly once.

7422 is the sum of its proper divisors that contain the digit 7.

7424 and its successor are both abundant.

7425 is an odd primitive abundant number.

7427 is the number of inequivalent asymmetric Ferrers graphs with 35 points.

7429 is the product of 3 consecutive primes.

7430 is the number of labeled commutative monoids of order 5.

7433 is a prime that remains prime if any digit is deleted.

7435 is a cubic star number.

7436 is the number of 6×6 alternating sign matrices.

7444 is a value of n for which |cos(n)| is smaller than any previous integer.

7447 is a palindrome in base 2 and in base 10.

7448 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

7456 is the number of inequivalent Ferrers graphs with 35 points.

7462 is the number of multigraphs with 26 vertices and 4 edges.

7464 is a structured hexagonal diamond number.

7465 = 54321 in base 6.

7469 is the smallest number that can not be written as the sum of 2 volumes of rectangular boxes with integer dimensions less than 21.

7471 is a centered cube number.

7473 is a Tribonacci-like number starting from 1, 1, and 1.

7475 has a sum of digits equal to its largest prime factor.

7480 is a value of n for which _2nC_n is divisible by n².

7485 is the number of conjugacy classes of the alternating group A₃₅.

7488 = (12 × 13 × 14 × 15 × 16) / (12 + 13 + 14 + 15 + 16) .

7490 has a square with the last 3 digits the same as the 3 digits before that.

7491 has a base 8 representation which is the reverse of its base 7 representation.

7494 is the sum of its proper divisors that contain the digit 4.

7496 = 777 + 44 + 9 + 6666.

7497 is a hendecagonal pyramidal number.

7499 is the smallest number whose 8^th power has 31 digits.

7500 is the order of a perfect group.

7508 would be prime if preceded and followed by a 1, 3, 7, or 9.

7509 has a 6^th root whose decimal part starts with the digits 1-9 in some order.

7512 is the sum of its proper divisors that contain the digit 5.

7515 has the property that the sum of its prime factors is equal to the product of its digits.

7519 is a member of the Fibonacci-type sequence starting with 1 and 7.

7524 is the number of rectangles with corners on an 12×12 grid of points.

7525 has a square with the last 3 digits the same as the 3 digits before that.

7528 is the number of ways, up to rotation and reflection, of dissecting a regular 14-gon into 12 triangles.

7531 has digits in arithmetic sequence.

7532 has a square comprised of the digits 0-7.

7535 has a square whose digits each occur twice.

7541 is an Eisenstein-Mersenne prime.

7542 is a value of n for which 4n and 7n together use each digit exactly once.

7546 is the number of series-reduced planted trees with 19 vertices.

7547 is the maximum number of regions a circle can be cut into by joining 21 points on the circumference with straight lines.

7549 is the largest known prime p where no numbers of the form p-n² are prime.

7551 is a value of n for which φ(n) + φ(n+1) divides σ(n) + σ(n+1).

7552 is the number of arrangements of 6 non-attacking queens on a 10×6 chessboard.

7557 is a palindrome that is the sum of the first 37 palindromes.

7560 is the smallest number with 64 divisors.

7561 is a Markov number.

7562 would be prime if preceded and followed by a 1, 3, 7, or 9.

7574 is the sum of consecutive squares in 2 ways.

7581 is the number of monotone Boolean functions of 5 variables.

7586 = 777 + 55 + 88 + 6666.

7588 is the smallest multiple of 28 whose digits add to 28.

7590 is a number whose sum of divisors is a 4^th power.

7595 is the number of simplicial polyhedra with 12 vertices.

7597 is a number whose sum of divisors is a 5^th power.

7600 is a substring of any power of itself.

7614 is a value of n for which n and 7n together use each digit 1-9 exactly once.

7615 is a value of n for which σ(n+1) = 2σ(n).

7617 is a Hexanacci number.

7618 has a cube that contains only digits 4 and smaller.

7620 is the number of multigraphs with 5 vertices and 14 edges.

7625 is a value of n for which σ(φ(n)) = 2σ(n).

7627 is a value of n for which σ(φ(n)) = 2σ(n).

7629 is a value of n for which n and 5n together use each digit 1-9 exactly once.

7632 is a value of n for which 5n and 6n together use each digit exactly once.

7635 is a centered tetrahedral number.

7639 is the number of rooted ternary trees with 13 vertices.

7647 is a Keith number.

7648 is the number of ways a 10×1 rectangle can be surrounded by 10×1 rectangles.

7650 can be written as the product of a number and its reverse in 2 different ways.

7651 is a value of n for which _2nC_n is not divisible by 3, 5, or 7.

7652 is a value of n for which n² and n³ use the same digits.

7654 has digits in arithmetic sequence.

7658 is the largest number known that does not have any digits in common with its cube.

7659 is the number of planar graphs with 22 vertices, all with degree 5 or more.

7663 is the product of two primes which are reverses of each other.

7664 is the Entringer number E(8,6).

7665 is a Kaprekar constant in base 2.

7667 is a palindrome in base 6 and in base 10.

7669 is the number of integers with complexity 31.

7672 = 777 + 6666 + 7 + 222.

7673 is the smallest number with the property that its first 8 multiples contain the digit 3.

7679 = 7 + 6666 + 7 + 999.

7680 is the number of possible rook moves on a 16×16 chessboard.

7681 is a Proth prime.

7683 is a truncated tetrahedral number.

7685 is the number of necklaces possible with 18 beads, each being one of 2 colors.

7686 is a value of n for which 7n and 9n together use each digit exactly once.

7688 is an Achilles number.

7692 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7693 is a value of n for which the sum of the first n primes is a palindrome.

7695 and its successor are both divisible by 4^th powers.

7698 has a square with the first 3 digits the same as the next 3 digits.

7700 is a value of n for which 2φ(n) = φ(n+1).

7703 has a 4^th power that is the sum of four 4^th powers.

7710 is the number of degree 17 irreducible polynomials over GF(2).

7712 is the number of necklaces (that can't be turned over) possible with 17 beads, each being one of 2 colors.

7713 is a value of n for which 4n and 9n together use each digit exactly once.

7714 is the sum of the first 28 squares.

7721 is the smallest value of n for which 3ⁿ contains 8 consecutive 3's.

7724 is the smallest number that can not be written using +, ×, and 5 Fibonacci numbers.

7727 is the index of a Fibonacci number whose first 9 digits are the digits 1-9 rearranged.

7732 and the two numbers before it and after it are all products of exactly 3 primes.

7734 is the sum of its proper divisors that contain the digit 8.

7736 is the number of labeled Eulerian digraphs with 5 vertices.

7738 has the property that dropping its first and last digits gives its largest prime factor.

7739 is a Padovan number.

7741 is the number of trees with 15 vertices.

7743 is the smallest number whose 9^th power has 35 digits.

7744 is the smallest known square with no isolated digits.

7745 and its reverse are both one more than a square.

7746 is the number permutations of {1,2,3,...,21} where adjacent numbers differ by no more than 2.

7752 is the generalized Catalan number C(14,5).

7754 is the number of binary cube-free words of length 21.

7755 is the index of a prime Woodall number.

7765 is the number of ways to tile a 7×5 rectangle with integer-sided squares.

7770 = ₃₇C₃.

7772 has a square root whose decimal part starts with the digits 1-9 in some order.

7773 is the number of stable patterns with 17 cells in Conway's game of Life.

7775 = 55555 in base 6.

7776 is a 5^th power whose digits are non-increasing.

7777 is a Kaprekar number.

7778 is the closest integer to 27^e.

7785 is a value of n for which 5n and 6n together use each digit exactly once.

7788 is the index of a triangular number containing only 3 different digits.

7792 has a square that is the sum of a cube and 5^th power.

7793 is the smallest prime so that it and the next 5 primes are all equal to 5 (mod 6).

7795 has the same digits as the 7795^th prime.

7799 is a value of n for which |cos(n)| is smaller than any previous integer.

7800 is the order of a non-cyclic simple group.

7803 is an Achilles number.

7805 is the maximum number of pieces a torus can be cut into with 35 cuts.

7807 is the maximum number of regions a cube can be cut into with 36 cuts.

7808 is the number of 4×4 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in a corner.

7810 has the property that its square is the concatenation of two consecutive numbers.

7811 is the number of ordered sequences of coins totaling 32 cents.

7812 = 222222 in base 5.

7820 is the Stirling number of the second kind S(17,15).

7821 is a value of n for which 2n and 9n together use each digit exactly once.

7824 is a value of n for which 5n and 7n together use each digit exactly once.

7825 is a rhombic dodecahedral number.

7826 is the number of necklaces possible with 6 beads, each being one of 6 colors.

7827 has a square whose digits each occur twice.

7835 would be prime if preceded and followed by a 1, 3, 7, or 9.

7846 is a factor of 7847784878497850.

7848 is the number of connected 5-regular graphs with 12 vertices.

7849 is the number of connected 6-regular graphs with 12 vertices.

7851 = 7777 + 8 + 55 + 11.

7852 = 1963 × 4, and each digit from 1-9 is contained in the equation exactly once.

7853 is the largest prime factor of 11! - 1.

7854 is a number whose sum of divisors is a 4^th power.

7856 and its successor are both the product of a prime and the 4^th power of a prime.

7860 is the number of nonisomorphic 3-state automata with binary inputs and outputs.

7874 is the smallest number n for which n concatenated with n+2 is a square.

7875 is an odd abundant number.

7880 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 26 stamps.

7882 is a structured pentagonal hexacontahedral number.

7884 is a value of n for which 2n and 5n together use each digit exactly once.

7887 is the index of a pentagonal number which is twice another pentagonal number.

7888 is a value of n where φ(n) is the product of the digits of n.

7890 is an icosahedral number.

7894 is a value of n for which n and 8n together use each digit 1-9 exactly once.

7895 is the number of multigraphs with 6 vertices and 11 edges.

7905 is a Kaprekar constant in base 2.

7908 has the same digits as the 7908^th prime.

7909 is a Keith number.

7912 is a weird number.

7913 is a value of n for which σ(n-1) = σ(n+1).

7917 is the number of partitions of 57 into distinct parts.

7919 is the 1000^th prime.

7920 is the order of the smallest sporadic group.

7921 is the square of a Fibonacci number.

7922 has the property that the sum of its prime factors is equal to the product of its digits.

7923 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7926 is the diameter of the earth in miles.

7928 is a Friedman number.

7931 is a heptagonal pyramidal number.

7932 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7936 is the 5^th tangent number.

7937 is the smallest number whose cube contains 5 consecutive 9's.

7939, when followed by any of its digits, is prime.

7941 = 7777 + 9 + 44 + 111.

7942 = 7777 + 99 + 44 + 22.

7946 = 7777 + 99 + 4 + 66.

7953 is the number of domino tilings of a 3×14 rectangle.

7954 is the smallest value of n for which 5ⁿ + n is prime.

7956 is a value of n for which n and 4n together use each digit 1-9 exactly once.

7957 is a Poulet number.

7958 = 8 × 9 × 10 × 11 + 8 + 9 + 10 + 11.

7960 is a structured deltoidal hexacontahedral number.

7964 is a value of n for which φ(n) = φ(reverse(n)).

7969 has a square that is formed by 3 squares that overlap by 1 digit.

7980 is the smallest number whose divisors contain every digit at least 7 times.

7983 is a Lucas 8-step number.

7986 = 11 × 22 × 33.

7992 can be written as the difference between two positive cubes in more than one way.

7993 is one less than twice its reverse.

7994 has a 5^th power that is closer to a cube than a square.

7997 is a palindrome in base 4 and in base 10.

7999, when followed by any of its digits, is prime.

8000 is the smallest cube which is also the sum of 4 consecutive cubes.