1800

1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5.

1800 is a pentagonal pyramidal number.

1800 is the sum of 10 consecutive primes: 1800 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199.

1800 is 5151 in base 7. It is 800 in base 15.

1800 has two representations as a sum of two squares: 1800 = 6² + 42² = 30² + 30².

1800 divides 49⁶ - 1.

Source: Prime Curios!

550

550 = 2 x 5 x 5 x 11.

550 is a pentagonal pyramidal number (A002411).

505 is 202101 in base 3. It is 1414 in base 7.

550 is the number of primes less than 4000 (A028505 and A038812).

550 is a divisor of 43⁴ - 1.

Source: What's Special About This Number?

936

936 = 2 x 2 x 2 x 3 x 3 x 13.

936 is an octagonal number (A000567) and a pentagonal pyramidal number (A002411).

936 is 12221 in base 5.

936³ = 820,025,856 = (820 + 02 + 58 + 56)³.

936 has a representation as a sum of two squares: 936 = 6² + 30².

936 is a number that can be expressed as the difference of the squares of primes in just one distinct way (A090781).

Source: What's Special About This Number?

196

196 = 2² x 7².

196 is the smallest square that contains a multidigit prime number as a substring.

196 = 14² is a perfect square.

196 is the difference of two square numbers: 196 = 50² - 48².

The consecutive squares 13² = 169 and 14² = 196 use the same digits; 31² = 961 also uses the same digits.

196 has a unique representation as a sum of three squares: 196 = 4² + 6² + 12².

196 is a pentagonal pyramidal number and a heptagonal pyramidal number.

It is conjectured that 196 is the lowest Lychrel number. It is the lowest number not known to produce a palindrome by repeated reversal and addition. The algorithm has been tested to more than 246 million digits without finding a palindrome, but no one has ever proved that it will never produce one.

The Mercedes-Benz W196 was an entry in the 1954 and 1955 Formula One car racing series, winning 9 of 12 races.

Source: Number Gossip

405

405 = 3⁴ x 5.

405 has a representation as a sum of two squares: 405 = 9² + 18².

405 is a pentagonal pyramidal number.

405 is 120000 in base 3 and 12111 in base 4. It is 500 in base 9.

405 is a tridecagonal number.

405 is the telephone area code for central Oklahoma.

Source: What's Special About This Number?

288

288 = 2⁵ x 3².

288 has a representation as a sum of two squares: 288 = 12² + 12².

288 has the representation 288 = 2⁸ + 32.

288 is a pentagonal pyramidal number.

288 is the smallest non-palindrome non-square that when multiplied by its reverse is a square: 288 x 882 = 254,016 = 504².

288 Glauke is an asteroid with an exceptionally slow rotation period of about 1200 hours.

Source: What's Special About This Number?

126

126 = 2 x 3² x 7.

126 is the sixth pentatope number.

126 is 99 in base 13.

126 is a decagonal number and a pentagonal pyramidal number.

126 is the number of prime days in a non-leap year.

The Ferrari 126C was Ferrari's first attempt at turbo-charged Formula 1 car.

Source: Number Gossip