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

Author

David W. Wilson

Keywords

• nonn

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

Programs

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 *)