A025315 Numbers that are the sum of 2 distinct nonzero squares in 5 or more ways.

5525, 8125, 9425, 10625, 11050, 12025, 12325, 13325, 14365, 15725, 16250, 17225, 17425, 18125, 18785, 18850, 19825, 21125, 21250, 22100, 22525, 23125, 23725, 24050, 24505, 24650, 25625, 25925, 26650, 26825, 27625, 28730, 28925, 29725, 31025, 31265

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Subsequence of A025296. But sequences A025315 and A025296 are different. 2*5^8 = 781250 = 625^2 + 625^2 (not distinct squares) = 425^2 + 775^2 = 365^2 + 805^2 = 191^2 + 863^2 = 125^2 + 875^2 is not in A025315. - Vaclav Kotesovec, Feb 27 2016

Numbers in A025296 but not in A025315 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q_1^8 or of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q_1^2*q_2^2 where p_i are primes of the form 4k+3 and q_1, q_2 are distinct primes of the form 4k+1. Thus 2*5^2*13^2 = 8450 is the smallest term in A025296 that is not in A025315. - 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 = 31265; 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, ?(# >= 5 &)]] (* _T. D. Noe, Apr 07 2011 *)