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ΑΡΙΘΜΟΙ 8001 - 9000

8001 is a Kaprekar constant in base 2.
8002 is the index of a triangular number containing only 3 different digits.
8003 has the property that if each digit is replaced by its square, the resulting number is a square.
8004 has a square with the first 3 digits the same as the next 3 digits.
8008 = ₁₆C₆.
8010 uses the same digits as π(8010).
8012 is the number of 3-connected planar maps with 18 edges.
8016 has a square with the last 3 digits the same as the 3 digits before that.
8022 uses the same digits as φ(8022).
8026 is the number of planar partitions of 19.
8032 is the number of congruency classes of triangles with vertices from a 15×15 grid of points.
8042 is the largest number known which cannot be written as a sum of 7 or fewer cubes.
8043 has a square whose digits each occur twice.
8045 is the number of 6-digit twin primes.

8051 is the number of partitions of 52 in which no part occurs only once.
8056 is the number of triangles of any size contained in the triangle of side 31 on a triangular grid.
8064 = (1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9) / (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9).
8071 is the number of connected graphs with 11 edges.
8074 is the trinomial coefficient T(12,6).
8077 is a value of n for which n² and n³ use the same digits.
8080 has a square root that has four 8's immediately after the decimal point.
8082 has a square comprised of the digits 1-8.
8083 is a value of n for which n concatenated with n-2 is square.
8085 is an odd primitive abundant number.
8087 is a Lucas 9-step number.
8089 is the pseudosquare modulo 13.
8090 is a Perrin number.
8092 is a Friedman number.
8100 is divisible by its reverse.
8103 is the closest integer to e⁹.
8104 is equal to the sum of its anti-divisors.
8118 is a strobogrammatic number.
8119 is an NSW number.
8121 is the smallest number whose cube contains seven 5's.
8125 is the smallest number that can be written as the sum of 2 squares in 5 ways.
8128 is the 4^th perfect number.
8129 is a member of the Fibonacci-type sequence starting with 2 and 7.
8135 is the 7^th central pentanomial coefficient.
8136 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
8149 is a value of n for which 2n and 7n together use each digit exactly once.
8152 is the number of symmetric arrangements of 8 non-attacking queens on a 8×8 chessboard.
8154 is a value of n for which |cos(n)| is smaller than any previous integer.
8156 has a cube that is only 24 away from a square.
8165 has a square that begins with four 6's.
8169 = 24507 / 3, and each digit is contained in the equation exactly once.
8170 is an enneagonal pyramidal number.
8174 is a value of n for which n and 8n together use each digit 1-9 exactly once.
8176 is a stella octangula number.
8178 is the number of ways 13 people can line up so that only one person has a taller person in front of him.
8179 is a value of n for which 4n and 5n together use each digit exactly once.
8180 is the maximum number of regions space can be divided into by 30 spheres.
8184 has exactly the same digits in 3 different bases.
8189 is the index of a triangular number containing only 3 different digits.
8190 is a harmonic divisor number.
8191 is a Mersenne prime.
8192 is the smallest non-trivial 13^th power.
8194 is the number of subsets of the 26^th roots of unity that add to 0.
8195 is the number of 17-ominoes with a horizontal or vertical line of symmetry.
8196 has a square whose digits each occur twice.
8198 is the index of a Fibonacci number whose first 9 digits are the digits 1-9 rearranged.
8200 = 8 + 2¹³ + 0 + 0.
8201 = 8 + 2¹³ + 0 + 1.
8202 = 8 + 2¹³ + 0 + 2.
8203 = 8 + 2¹³ + 0 + 3.
8204 = 8 + 2¹³ + 0 + 4.
8205 = 8 + 2¹³ + 0 + 5.
8206 = 8 + 2¹³ + 0 + 6.
8207 = 8 + 2¹³ + 0 + 7.
8208 is a narcissistic number.
8209 = 8 + 2¹³ + 0 + 9.
8217 is a centered icosahedral number.
8219 is a value of n for which 4n and 5n together use each digit exactly once.
8220 and its reverse are both the averages of twin primes.
8221 has a base 3 representation that begins with its base 6 representation.
8225 are the first 4 digits of 8⁸²²⁵.
8226 is the sum of its proper divisors that contain the digit 4.
8229 has a square whose digits each occur twice.
8230 is the number of necklaces with 8 beads, each one of 4 colors.
8241 is a value of n for which n has σ(n) / reverse(n) divisors.
8242, when concatenated with one less than it, is square.
8256 is the number of different arrangements (up to rotation and reflection) of 30 non-attacking bishops on a 16×16 chessboard.
8257 is the sum of the squares. of the first 14 primes.
8258 is the number of different positions in Connect Four after 6 moves.
8265 has a 7^th root whose decimal part starts with the digits 1-9 in some order.
8269 is a Cuban prime.
8280 is the smaller number in a Ruth-Aaron pair.
8281 is the only 4-digit square whose two 2-digit pairs are consecutive.
8283 has a base 8 representation which is the reverse of its base 7 representation.
8284 is a structured truncated cubic number.
8292 is the number of anisohedral 22-iamonds.
8294 has the property that dropping its first and last digits gives its largest prime factor.
8299 is a value of n for which reverse(φ(n)) = φ(reverse(n)).
8303 = 12345 in base 9.
8304 is the number of subsets of the 18^th roots of unity that add to a real number.
8305 has the same digits as the 8305^th prime.
8313 is a dodecagonal pyramidal number.
8316 is the sum of 3 consecutive cubes.
8317 is the number of trees on 33 vertices with diameter 4.
8320 is the number of subsets of {1, 1/2, 1/3, ... 1/42} that sum to an integer.
8321 is a Poulet number.
8338 is a value of n so that n(n+4) is a palindrome.
8340 is a value of n so that (n-1)² + n² + (n+1)² is a palindrome.
8342 is the number of partitions of 53 in which no part occurs only once.
8345 is the smallest number in base 6 to have 6 different digits.
8349 is the number of partitions of 32.
8350 is the trinomial coefficient T(10,1).
8351 has the same digits as the 8351^st prime.
8353 is the smallest number whose 4^th power contains 5 consecutive 6's.
8355 has the same digits as the 8355^th prime.
8360 has a square whose digits each occur twice.
8361 is a Leyland number.
8363 is the number of 5-digit primes.
8368 has a 6^th power whose first few digits are 34334444....
8369 is the largest prime factor of 2 × 3 × 5 × 7 × 11 × 13 × 17 - 1.
8372 is a hexagonal pyramidal number.
8373 has a 4^th power that is the sum of four 4^th powers.
8375 is the smallest number which has equal numbers of every digit in bases 2 and 6.
8378 has a 10^th root whose decimal part starts with the digits 1-9 in some order.
8379 is a value of n for which 5n and 8n together use each digit exactly once.
8382 is the index of a triangular number containing only 3 different digits.
8384 is the maximum number of 13^th powers needed to sum to any number.
8385 is a structured great rhombicubeoctahedral number.
8388 and its reverse are both the averages of twin primes.
8390 is the number of linear spaces on 7 labeled points.
8392 is a value of n for which n, n+1, n+2, and n+3 have the same number of divisors.
8393 is a value of n for which σ(reverse(n)) = φ(n).
8394 is a value of n for which n and 8n together use each digit 1-9 exactly once.
8396 does not occur in its factorial in base 2.
8397 is the largest known composite number n so that _3nC_n = 3ⁿ (mod n).
8398 is the 10^th super-ballot number.
8400 is the number of legal queen moves in Chess.
8401 has the property that if each digit is replaced by its square, the resulting number is a square.
8403 = 33333 in base 7.
8404 is the number of connected graphs with 9 vertices and 13 edges.
8406 is the number of ways to divide 8 black and 8 white beads into piles.
8408 has 8408 / π(8408) divisors.
8411 would be prime if preceded and followed by a 1, 3, 7, or 9.
8415 is an odd primitive abundant number.
8418 is the number of necklaces possible with 11 beads, each being one of 3 colors.
8419 is a value of n for which n and 8n together use each digit 1-9 exactly once.
8420 is the number of symmetric ways to fold a strip of 20 stamps.
8421 = 1111 in base 20.
8428 is the number of quasi-triominoes that fit inside a 15×15 grid.
8430 and its reverse are both the averages of twin primes.
8433 has a 4^th power that is the sum of four 4^th powers.
8436 = ₃₈C₃.
8439 is a value of n for which n and 8n together use each digit 1-9 exactly once.
8440 is a truncated square pyramid number.
8441 is the sum of the cubes of 3 consecutive primes.
8442 is the smallest value of n for which the numbers n-7 through n+7 can not be written as the sum of 2 squares.
8451 is the number of 3×3 matrices in base 3 with determinant 0.
8455 is the trinomial coefficient T(20,16).
8459 is a value of n so that n(n+4) is a palindrome.
8461 is the smallest number whose 9^th power starts with 5 identical digits.
8463 is the smaller number in a Ruth-Aaron pair.
8464 is the number of different products of subsets of the set {1, 2, 3, ... 17}.
8465 = 4³ + 5⁴ + 6⁵.
8467 has a 9^th root whose decimal part starts with the digits 1-9 in some order.
8469 is a value of n for which 2n and 3n together use each digit exactly once.
8470 is the number of conjugacy classes in the automorphism group of the 17 dimensional hypercube.
8472 is the maximum number of pieces a torus can be cut into with 36 cuts.
8473 is a centered octahedral number.
8474 is the maximum number of regions a cube can be cut into with 37 cuts.
8475 is the first of four consecutive squareful numbers.
8477 = 1⁰ + 2¹ + 3² + 4³ + 5⁴ + 6⁵.
8481 is a Poulet number.
8484 is the reciprocal of the sum of the reciprocals of 13332 and its reverse.
8486 = 888 + 44 + 888 + 6666.
8492 is the number of arrangements of 5 non-attacking queens on a 11×5 chessboard.
8493 has a 4^th power that is the sum of four 4^th powers.
8494 is a value of n for which σ(n) = φ(n) + φ(n-1) + φ(n-2).
8497 is the number of anisohedral 17-hexes.
8499 is the sum of the squares of 3 consecutive primes.
8505 = 21!!!!!!.
8506 is the number of isomers of C₁₃H₂₆ without any double bonds.
8509 is a value of n for which |cos(n)| is smaller than any previous integer.
8510 is a value of n for which the sum of the first n primes is a palindrome.
8512 is the number of non-intersecting rook paths joining opposite corners of a 5×5 chessboard.
8515 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
8517 has a 4^th power that is the sum of four 4^th powers.
8521 is a prime that is the average of two 4^th powers.
8523 is the first of four consecutive squareful numbers.
8525 has a square whose digits each occur twice.
8526 is a Rhonda number.
8533 has the property that dropping its first and last digits gives its largest prime factor.
8538 is the sum of its proper divisors that contain the digit 4.
8541 is a value of n so that n(n+6) is a palindrome.
8545 is the number of ways to stack 36 boxes in a line so that each box lies on the table or on a box next to 2 boxes.
8547 is a divisor of 111111.
8548 is the sum of the squares of 4 consecutive primes.
8549 has the property that the sum of its proper divisors is the sum of the squares of its digits.
8555 is the sum of the first 29 squares.
8558 is a Schröder number.
8559 has a square comprised of the digits 1-8.
8562 is the sum of its proper divisors that contain the digit 4.
8563 is the index of a triangular number containing only 3 different digits.
8568 = ₁₈C₅.
8569 is a centered dodecahedral number.
8571 shares 3 consecutive digits with one of its prime factors.
8575 is an Achilles number.
8576 can be written as the sum of 2, 3, 4, or 5 positive cubes.
8577 has a 4^th power that is the sum of four 4^th powers.
8578 appears inside its 4^th power.
8579 divides 1¹ + 2² + 3³ + ^{. . .} + 8579⁸⁵⁷⁹.
8580 is the number of subsets of the 28^th roots of unity that add to 1.
8582 is the number of monoids of order 7 with 5 idempotents.
8586 has exactly the same digits in 3 different bases.
8591 is the number of partitions of 42 that do not contain 1 as a part.
8599 is the number of forests with 14 vertices.
8602 is the generalized Catalan number C(20,4).
8610 = 400 + 401 + . . . + 420 = 421 + 422 + . . . + 440.
8614 and its prime factors contain every digit from 1-9 exactly once.
8626 is the number of asymmetric trees with 13 vertices.
8627 is a value of n for which 2n and 7n together use each digit exactly once.
8631 is a value of n for which 3n and 7n together use each digit exactly once.
8633 is the product of two consecutive primes.
8637 has a 4^th power that is the sum of four 4^th powers.
8638 = 7 + 77 + 777 + 7777.
8640 = 2! × 3! × 6!.
8641 is the number of ways to tile a 3×25 rectangle with 3×1 rectangles.
8642 has digits in arithmetic sequence.
8646 divides 2⁸⁶⁴⁶ + 2.
8649 is a value of n for which 2n and 7n together use each digit exactly once.
8657 is the number of ways to tile a 4×30 rectangle with 4×1 rectangles.
8658 is the sum of the first 4 perfect numbers.
8663 has the property that if each digit is replaced by its square, the resulting number is a square.
8664 = 888 + 6666 + 666 + 444.
8666 has a 9^th root whose decimal part starts with the digits 1-9 in some order.
8669 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 18 stamps.
8670 is a value of n for which n!! - 1 is prime.
8672 is the number of 14-ominoes that tile the plane by translation.
8680 has a base 5 representation that ends with its base 7 representation.
8681 has a base 5 representation that ends with its base 7 representation.
8682 has a base 5 representation that ends with its base 7 representation.
8683 has a base 5 representation that ends with its base 7 representation.
8684 has a base 5 representation that ends with its base 7 representation.
8688 is the number of possible configurations of pegs (up to symmetry) after 26 jumps in solitaire.
8695 is a centered tetrahedral number.
8697 is a structured octagonal anti-diamond number.
8698 is a strobogrammatic number.
8703 has a cube that is the sum of 3 positive cubes.
8712 is 4 times its reverse.
8714 is the number of ways 24 people around a round table can shake hands in a non-crossing way, up to rotation.
8718 is the smallest n for which Σ_k≤n 1/(k ln k) ≥ 3.
8721 is a value of n for which φ(n) and σ(n) are square.
8732 has exactly the same digits in 3 different bases.
8736 is the smallest number that appears in its factorial 10 times.
8739 is a permutation of the sum of its proper divisors.
8743 is a number whose sum of divisors is a 4^th power.
8744 is the number of subsets of {1,2,3,...,17} that have a sum divisible by 15.
8745 is the number of ways to divide a 13×13 grid of points into two sets using a straight line.
8748 is the largest number whose prime factors add to 25.
8751 is a perfect totient number.
8753 = 88 + 7777 + 555 + 333.
8758 = 88 + 7777 + 5 + 888.
8761 is the number of ordered partitions of 25 into distinct parts.
8763 and its successor have the same digits in their prime factorization.
8765 has digits in arithmetic sequence.
8771 2⁴ + 3⁴ + 4⁴ + 5⁴ + 6⁴ + 7⁴ + 8⁴.
8772 is the sum of the first eight 4^th powers.
8778 is both a triangular number and 3 times a triangular number.
8779 is is the largest prime factor of 100000000001.
8781 is the closest integer to 18^π.
8784 is a value of n for which 2n and 5n together use each digit exactly once.
8785 is the number of 13-iamonds without holes.
8788 is an Achilles number.
8793 is a value of n for which n!!! - 1 is prime.
8796 is a value of n for which 5n and 7n together use each digit exactly once.
8797 is a structured hexagonal diamond number.
8801 is the magic constant of a 26×26 magic square.
8808 is the number of partitions of 58 into distinct parts.
8810 has a square whose digits each occur twice.
8813 is the number of chiral invertible knots with 14 crossings.
8814 is the number of multigraphs with 27 vertices and 4 edges.
8816 is a value of n for which reverse(φ(n)) = φ(reverse(n)).
8819 is the smallest number whose square begins with four 7's.
8820 is a highly abundant number.
8821 has the property that if each of its digits is replaced by its cube, the result is a square.
8826 is the sum of its proper divisors that contain the digit 4.
8829 is a value of n for which 6n and 7n together use each digit exactly once.
8830 is the number of lines passing through at least 2 points of an 14×14 grid of points.
8831 would be prime if preceded and followed by a 1, 3, 7, or 9.
8833 = 88² + 33².
8835 is the index of a triangular number containing only 3 different digits.
8837 is the smallest number that can not be written as the sum of 3 volumes of rectangular boxes with integer dimensions less than 17.
8838 and its reverse are both the averages of twin primes.
8840 is the number of triangles of any size contained in the triangle of side 32 on a triangular grid.
8843 is the smallest number that can not be written as the sum of 2 volumes of rectangular boxes with integer dimensions less than 22.
8846 is the number of divisors of the 20^th perfect number.
8854 is the number of possible rows in a 20×20 crossword puzzle.
8855 is a Lucas-Carmichael number.
8856 is the number of subsets of {1,2,3,...,16} that have an integer average.
8857 is a structured truncated tetrahedral number.
8860 is the smallest number n so that n+3, n²+3², n⁴+3⁴, and n⁸+3⁸ are all prime.
8864 is a value of n for which |cos(n)| is smaller than any previous integer.
8867 is the smallest prime with multiplicative persistence 6.
8874 has a square that is the concatenation of two consecutive even numbers.
8878 is the number of intersections when all the diagonals of a regular 23-gon are drawn.
8883 does not occur in its factorial in base 2.
8887 is a value of n for which σ(n) is a repdigit.
8888 is a repdigit.
8892 is a betrothed number.
8902 is the number of possibilities for the first 1.5 moves in Chess.
8905 multiplied by its successor gives a number concatenated with itself.
8910 is divisible by its reverse.
8911 is a Carmichael number.
8913 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 27 stamps.
8922 is the sum of its proper divisors that contain the digit 4.
8923 is the numerator of 1 / 1¹ + 1 / 2² + 1 / 3³ + 1 / 4⁴.
8925 is an odd primitive abundant number.
8930 = 8888 + 9 + 33 + 0.
8931 = 8888 + 9 + 33 + 1.
8932 = 8888 + 9 + 33 + 2.
8933 = 8888 + 9 + 33 + 3.
8934 = 8888 + 9 + 33 + 4.
8935 = 8888 + 9 + 33 + 5.
8936 = 8888 + 9 + 33 + 6.
8937 = 8888 + 9 + 33 + 7.
8938 = 8888 + 9 + 33 + 8.
8939 = 8888 + 9 + 33 + 9.
8942 is a value of n for which n and 8n together use each digit 1-9 exactly once.
8944 is the sum of the cubes of the first 7 primes.
8950 has a 4^th root whose decimal part starts with the digits 1-9 in some order.
8953 is the 10^th central trinomial coefficient.
8954 is the first of four consecutive squareful numbers.
8958 has a 4^th power whose product of digits is also a 4^th power.
8959 is the smallest multiple of 31 whose digits add to 31.
8964 is the smallest number with the property that its first 6 multiples contain the digit 8.
8965 is a value of n for which n² and n³ use the same digits.
8968 is a strobogrammatic number.
8970 = 8 + 9⁴ + 7⁴ + 0.
8971 = 8 + 9⁴ + 7⁴ + 1.
8972 = 8 + 9⁴ + 7⁴ + 2.
8973 = 8 + 9⁴ + 7⁴ + 3.
8974 = 8 + 9⁴ + 7⁴ + 4.
8975 = 8 + 9⁴ + 7⁴ + 5.
8976 = 8 + 9⁴ + 7⁴ + 6.
8977 = 8 + 9⁴ + 7⁴ + 7.
8978 = 8 + 9⁴ + 7⁴ + 8.
8979 = 8 + 9⁴ + 7⁴ + 9.
8980 is a value of n for which the first n binary digits of π form a prime.
8982 uses the same digits as φ(8982).
8989 is a Delannoy number.
8991 is the smallest number so that it and its successor are both the product of a prime and the 5^th power of a prime.
8993 is a Huay rhombic dodecahedral number.
8999 is the smallest number whose digits add to 35.
9000 is the index of a triangular number containing only 3 different digits.