1521

1521 = 3 x 3 x 13 x 13.

1521 is a perfect square: 1521 = 39².

1521 is the smallest number that can be written as the sum of four distinct cubes in three ways: 1521 = 11³ + 5³ + 4³ + 1³ = 10³ + 8³ + 2³ + 1³ = 9³ + 8³ + 6³ + 4³.

1521 has a representation as a sum of two squares: 1521 = 15² + 36².

1521 is a divisor of 22³ - 1.

1521 is a centered octagonal number.

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!

121

121 = 11 x 11.

121 is the smallest multidigit palindromic square. It is also the smallest palindromic composite such that some permutation of digits is prime. It is the only odd palindromic square with an odd number of digits that is divisible by a palindromic prime number with an even number of digits.

121 is a perfect square. It is also a centered octagonal number and a centered dodecagonal number.

Every number greater than 121 is the sum of distinct primes of the form 4n + 1.

121 is 11111 in base 3.

121 is the maximum number of regions into which 15 lines divide a plane.

121 can be expressed as the sum of a prime and its reversal for exactly three distinct primes: 121 = 29 + 92 = 47 + 74 = 83 + 38.

121 = 1 + 3¹ + 3² + 3³ + 3⁴.

121 is the number of points required to win a standard game of cribbage.

Source: Prime Curios!

361

361 = 19 x 19.

361 is a centered triangular number (A005448). It is also a centered octagonal number (A016754) and a centered decagonal number (A062786).

The representations of 361 in bases 2, 3, 4, 5, 6, 8, 9, and 10 all end in 1. It is 551 in base 8 and 441 in base 9. It is 121 in base 18.

361 is a square that remains a square when the last digits is removed (A023110).

361 and 361² (130321) have the same digit sum (A058369): 3 + 6 + 1 = 10 = 1 + 3 + 0 + 3 + 2 + 1.

The game of Go is played on a grid of 19 x 19 lines, which produces 361 intersections on the game board.

Source: On-Line Encyclopedia of Integer Sequences

841

841 = 29 x 29.

841 is a centered square number. It is also a centered heptagonal number and a centered octagonal number.

841 has a representation as a sum of two squares: 841 = 20² + 21². It is the sum of two consecutive squares.

841 is the hypotenuse of a primitive Pythagorean triple: 841² = 41² + 840².

841 is the smallest 3-digit square whose digits are decreasing.

841 is the smallest binary prime square. It's a perfect square whose binary representation (1101001001) considered as a decimal is a prime number.

841 is a divisor of 41⁴ - 1.

Source: Number Gossip

225

225 = 3² x 5².

225 = 15². 225 is the smallest square that starts with two identical digits.

225 is the smallest square whose external digits (25) form a square, and whose internal digits (2) form a prime.

225 is the only three-digit square with all prime digits.

225 has a representation as a sum of two squares: 225 = 9² + 12².

225 is a divisor of 26² - 1.

225 is an octagonal number. It is also a centered octagonal number.

A Scrabble board has 225 squares.

Source: Number Gossip

289

289 = 17².

289 is the largest 3-digit square with increasing digits.

289 has a representation as a sum of two squares: 289 = 8² + 15².

289 is the hypotenuse of a primitive Pythagorean triple: 289² = 161² + 240².

289 is a centered octagonal number.

The Ford Mustang 289 was a high-performance version of the car in the 1960s.

Source: Number Gossip

625

625 = 5⁴. It is a perfect fourth power.

Two fourth powers use the same digits: 5⁴ = 625 and 4⁴ = 256.

625 has two representations as a sum of two squares: 625 = 7² + 24² = 15² + 20².

625 is the hypotenuse of a primitive Pythagorean triple: 625² = 336² + 527².

625 is a centered octagonal number.

625 is an automorphic number.

According to a 2010 White House news release, 625 people lost their health insurance every hour in 2009.

Source: What's Special About This Number?