A025318 Numbers that are the sum of 2 distinct nonzero squares in 8 or more ways.

27625, 32045, 40885, 45305, 47125, 55250, 58565, 60125, 61625, 64090, 66625, 67405, 69745, 71825, 77285, 78625, 80665, 81770, 86125, 87125, 90610, 91205, 93925, 94250, 98345, 98605, 99125, 99905, 101065, 107185, 110500, 111605, 112625, 114985

Offset

1,1

Comments

Subsequence of A025299. But sequences A025318 and A025299 are different. 2*5^14 = 12207031250 = 7285^2 + 110245^2 = 15625^2 + 109375^2 = 23875^2 + 107875^2 = 45625^2 + 100625^2 = 53125^2 + 96875^2 = 60319^2 + 92567^2 = 71975^2 + 83825^2 = 78125^2 + 78125^2 (not distinct squares) is not in A025318. - Vaclav Kotesovec, Feb 27 2016

Numbers in A025299 but not in A025318 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q_1^14 or of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q_1^2*q_2^4 where p_i are distinct primes of the form 4k+3 and q_1, q_2 are distinct primes of the form 4k+1. Thus 2*5^4*13^2 = 211250 is the smallest term in A025299 that is not in A025318. - Chai Wah Wu, Feb 27 2016

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sums of squares

Mathematica

nn = 114985; t = Table[0, {nn}]; lim = Floor[Sqrt[nn - 1]]; Do[num = i^2 + j^2; If[num <= nn, t[[num]]++], {i, lim}, {j, i - 1}]; Flatten[Position[t, _?(# >= 8 &)]] (* T. D. Noe, Apr 07 2011 *)

Crossrefs

Sequence in context: A025298 A025317 A025299 * A025291 A025309 A097244

Adjacent sequences: A025315 A025316 A025317 * A025319 A025320 A025321

Keyword

nonn

Author

David W. Wilson

Status

approved