895

895 = 5 x 179.

895 is a Woodall number. It has the form 2ⁿ n - 1 for n = 7 (A003261).

895 is a Smith number (A006753). The sum of the digits of 895 equals the sum of the digits of its prime factors. It is also the smallest multiple of five with a digit sum of 22 (A069534).

895 is a number that has no more than one zero in its binary representation (A089633 and A030130): 1101111111.

895 and the 895th prime (6967) have only the digit 9 in common (A107940).

Every base 5 digit of 895 (12040) is a base 9 digit of 895 (1204) (A037396).

Source: What's Special About This Number?

562

562 = 2 x 281.

562!/265! - 1 is a prime.

562 is the maximum number of regions into which 33 lines divide a plane. 562 is also the maximum number of regions a circle can be cut into by joining 11 points on the circumference with straight lines.

562 is the sum of 12 consecutive primes: 562 = 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71.

562 is a Smith number.

562 has a representation as a sum of two squares: 562 = 11² + 21².

Source: Prime Curios!

922

922 = 2 x 461.

922 is 1234 in base 9 (A048441).

The sum of 922 and its reversal is a prime: 922 + 229 = 1151.

922 is the middle number of three consecutive semiprimes (A086005): 921, 922, and 923.

922 is a Smith number (A006753).

922 has a representation as a sum of two squares: 922 = 9² + 29².

Source: What's Special About This Number?

454

454 = 2 x 227.

454 is the largest number known that cannot be written as a sum of seven or fewer cubes (A018889).

454 is a Smith number (A006753). The sum of its digits (4 + 5 + 4 = 13) is equal to the sum of the digits of its prime factors (2 + 2 + 2 + 7 = 13).

1 + 8 + 10 + 17 = 36 = 2 + 5 + 13 + 16
1² + 8² + 10² + 17² = 454 = 2² + 5² + 13² + 16²
1³ + 8³ + 10³ + 17³ = 6426 = 2³ + 5³ + 13³ + 16<sup>3

454 is 383 in base 11 (A029966) and 246 in base 14.</sup>

Source: What's Special About This Number?

729

729 = 3 x 3 x 3 x 3 x 3 x 3 = 3⁶. It is a perfect sixth power.

729 is a centered octagonal number.

728 and 729 are consecutive Smith numbers, so they are known as Smith brothers.

729 is the smallest odd cube represented as the sum of two prime numbers: 729 = 2 + 727.

729 is a cube that is the sum of three cubes: 729 = 9³ = 1³ + 6³ + 8³.

729 = 27² = (1 + 2 + 2 + 2 + 4 + 4 + 4 + 8)² = 1³ + 2³ + 2³ + 2³ + 4³ + 4³ + 4³ + 8³.

729 is 1331 in base 8 and 121 in base 26.

Source: Prime Curios!

391

391 = 17 x 23.

391 is a Smith number (A0906753). The sum of its digits (3 + 9 + 1 = 13) equals the sum of the digits of its prime factors (1 + 7 + 2 + 3 = 13).

391 is a centered pentagonal number (A005891).

391 is 474 in base 9 (A029955).

391 is a substring of 2³⁹¹ (A032740).

391, 393, and 395 are all semiprimes (A092125), between the prime numbers 389 and 397.

Source: On-Line Encyclopedia of Integer Sequences

958

958 = 2 x 479.

958 is the number of 3-colorable graphs with 5 vertices (A084279).

958 is a Smith number (A006753); the sum of its digits equals the sum of the digits of its prime factors: 9 + 5 + 8 = 2 + 4 + 7 + 9 = 22.

958² = 917764 and 959² = 919681 have the same digit sum (A202089): 34.

Source: What's Special About This Number?

728

728 = 2 x 2 x 2 x 7 x 13. It is the smallest number n where n and n + 1 are both products of five or more primes.

728 is 222222 in base 3 and 888 in base 9.

Consecutive Smith numbers are called Smith brothers: 728 is the smaller brother of the smallest pair (728 and 729) of Smith brothers. The sum of its digits is equal to the sum of the digits of its prime factors: 7 + 2 + 8 = 2 + 2 + 2 + 7 + 1 + 3 = 17.

728 is the sum of two distinct positive cubes: 728 = 8³ + 6³.

728 is the number of nodes in a regular 13-gon with all diagonals drawn.

Source: Number Gossip

438

438 = 2 x 3 x 73.

438 is a Smith number because the sum of its digits is equal to the sum of the digits of its prime factors: 4 + 3 + 8 = 2 + 3 + 7 + 3 = 15.

438 is 110110110 in base 2 (binary) and 666 in base 8. It is 3223 in base 5 and 141 in base 19.

438 divides 65⁶ - 1.

438 is the sum of 10 positive 5th powers: 438 = 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵.

The term "438 match" or "438 game" has been used by cricket news media to describe the famous 2006 One Day International in which Australia scored a world record 434 in their innings, only to see South Africa respond in their innings with 438.

Source: What's Special About This Number?

706

706 = 2 x 353.

706 has a representation as a sum of two squares: 706 = 9² + 25².

706 is 424 in base 13.

706 is a Smith number because the sum of its digits is equal to the sum of the digits of its factorization: 7 + 0 + 6 = 2 + 3 + 5 + 3 = 13.

706 is the sum of two nonzero fourth powers: 706 = 5⁴ + 3⁴.

The USS Albuquerque (SSN-706) was an attack submarine that was launched in 1982 and remains in active service.

Source: Wikipedia

166

166 = 2 x 83.

166 is a centered triangular number.

166 is the smallest number such that the number and its reversal are both congruent to 1 mod p for the same set of distinct odd primes: 166 = 661 = 1 mod (3, 5, 11).

166 is the smallest Smith number that is prime when reversed (661), turned upside down (991), and reversed-then-turned-upside-down (199). You get the next case by inserting a zero between the digits: 10606.

U-166 was the only German submarine lost in the Gulf of Mexico.

Source: Prime Curios!

654

654 = 2 x 3 x 109.

654 has a square that is the sum of a cube and fifth power.

The sum 327 + 654 = 981 is one of only four cases in which the equality n + 2n = 3n uses each of the nine digits 1 to 9 once (n = 192, 219, 273, and 327).

654 is 545 in base 11.

654 is a Smith number. The sum of its digits is equal to the sum of the digits of its prime factors: 6 + 5 + 4 = 2 + 3 + 1 + 0 + 9 = 15.

The Auburn Company produced the Auburn 654 automobile in 1936, the year the company went out of business.

Source: What's Special About This Number?

483

483 = 3 x 7 x 23.

12 x 483 = 5796 and 42 x 138 = 5796. Each equality uses each of the nine digits, 0 to 9, exactly once.

185,472 = 672 x 276 = 384 x 483.

483 is a Smith number because the sum of its digits is equal to the sum of the digits of its prime factors: 4 + 8 + 3 = 3 + 7 + 2 + 3 = 15.

WP 483 is a Western Pacific Railroad caboose located at the Western Pacific Railroad Museum (Feather River Railroad Society) in Portola, California.

Source: Numeropedia

852

852 = 2² x 3 x 71.

852 is a pentagonal number.

852 is the number of 6-colorable connected graphs with seven vertices.

852 is a Smith number.

NGC 852 is a galaxy in the constellation Eridanus.

Source: What's Special About This Number?

915

915 = 3 x 5 x 61.

915 is a Smith number. The sum of its digits equals the sum of the digits of its prime factors: 9 + 1 + 5 = 3 + 5 + 6 + 1 = 15.

915 is 4123 in base 6, 555 in base 13, and 393 in base 16.

915 is the number of primes less that 10⁴ that do not contain the digit 8.

915 is a telephone area code in Texas for the area around El Paso.

Source: Positive Integers

825

825 = 3 x 5² x 11.

825 is the number of legal ways to add two sets of parentheses to a product of nine variables.

825 is a Smith number. The sum of its digits is equal to the sum of the digits in its prime factorization: 8 + 2 + 5 = 3 + 5 + 5 + 1 + 1.

825 is the sum of six positive fifth powers: 825 = 3⁵ + 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵.


Asteroid 825 Tanina was discovered in 1916 and has a diameter of about 11 kilometers.

Source: What’s Special About This Number?

526

526 = 2 x 263.

526 is the number of ways to cut an 8-by-8 chessboard into two pieces with equal areas using a cut that travels only up and right.

526 is a Smith number. It a composite number such that the sum of its digits is equal to the sum of its prime factors: 5 + 2 + 6 = 2 + 2 + 6 + 3 = 13.

526 and 527 are both the products of two primes: 526 = 2 x 263 and 527 = 17 x 31.


526 is a centered pentagonal number.


Source: What’s Special About This Number?

634

634 = 2 x 317.

634 is a Smith number. The sum of its digits equals the sum of the digits appearing in its prime divisors: 6 + 3 + 4 = 2 + 3 + 1 + 7 = 13.

The fifth root of 634 has a decimal part that begins with the digits 634.

634 has a representation as a sum of two squares: 634 = 3² + 25².

634 Ute is an asteroid discovered in 1907.

Source: Number Gossip

85

85 = 5 x 17.

85 is a Smith number because the sum of its digits is equal to sum of the digits in its prime factorization: 8 + 5 = 13 = 5 + 1 + 7.

85 is a centered triangular number. Such a number can be represented by a dot in the center, with all other dots surrounding the center in successive triangular layers. The first few triangular numbers are: 1, 4, 10, 19, 31, 46, 64, 85, 109, . . .

85 is the largest known n for which 1² + 2² + 3² + . . . + n² = 1 + 2 + 3 + . . . + m has a solution.

There are 85 ways to tie a tie, according to a book by Thomas Fink and Yong Mao.

Sources: Wolfram MathWorld ; What's Special About This Number?