Number of the day: 229585

Arthur Cayley was born on this day 196 years ago.

Properties of the number 229585:

229585 is a cyclic number.
229585 = 5 × 17 × 37 × 73 is the 209187^th composite number and is squarefree.
229585 has 4 distinct prime factors, 16 divisors, 25 antidivisors and 165888 totatives.
229585 has an emirp digit sum 31 in base 10.
229585 = 114793² - 114792² = 22961² - 22956² = 6761² - 6744² = 3121² - 3084² = 1609² - 1536² = 1393² - 1308² = 713² - 528² = 497² - 132² is the difference of 2 nonnegative squares in 8 ways.
229585 is the sum of 2 positive triangular numbers.
229585 is the difference of 2 positive pentagonal numbers in 7 ways.
229585 = 297² + 376² = 159² + 452² = 236² + 417² = 88² + 471² = 324² + 353² = 192² + 439² = 144² + 457² = 12² + 479² is the sum of 2 positive squares in 8 ways.
229585 = 3² + 70² + 474² is the sum of 3 positive squares.
229585² = 156585² + 167900² = 108040² + 202575² = 36500² + 226665² = 146775² + 176540² = 81585² + 214600² = 7575² + 229460² = 121540² + 194775² = 51800² + 223665² = 23540² + 228375² = 147852² + 175639² = 118193² + 196824² = 82896² + 214097² = 106799² + 203232² = 35113² + 226884² = 40369² + 226008² = 143736² + 179023² = 122729² + 194028² = 53167² + 223344² = 159432² + 165199² = 97236² + 207977² = 24528² + 228271² = 155857² + 168576² = 92759² + 210012² = 19633² + 228744² = 131616² + 188113² = 63492² + 220631² = 11496² + 229297² = 137751² + 183668² = 129064² + 189873² = 70737² + 218416² = 118048² + 196911² = 47804² + 224553² = 27608² + 227919² = 90321² + 211072² = 16983² + 228956² = 58191² + 222088² = 150960² + 172975² = 114665² + 198900² = 86700² + 212585² = 74460² + 217175² is the sum of 2 positive squares in 40 ways.
229585² is the sum of 3 positive squares.
229585 is a proper divisor of 1511⁸ - 1.

The number 229585 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A218135: Norm of coefficients in the expansion of 1 / (1 - x - 2*I*x^2), where I^2=-1.
A255214: Number of partitions of n^2 into at most 10 square parts.