A025314 Numbers that are the sum of 2 distinct nonzero squares in 4 or more ways.

1105, 1625, 1885, 2125, 2210, 2405, 2465, 2665, 3145, 3250, 3445, 3485, 3625, 3770, 3965, 4225, 4250, 4420, 4505, 4625, 4745, 4810, 4930, 5125, 5185, 5330, 5365, 5525, 5785, 5945, 6205, 6290, 6305, 6409, 6500, 6565, 6625, 6890, 6970, 7085, 7225, 7250

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Subsequence of A025295. But sequences A025295 and A025314 are different, A025295(346) = 31250 = 175^2 + 25^2 = 161^2 + 73^2 = 155^2 + 85^2 = 125^2 + 125^2 (not distinct squares) is not in A025314. - Vaclav Kotesovec, Feb 27 2016

Numbers in A025295 but not in A025314 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^6 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^6 = 31250 is the smallest term in A025295 that is not in A025314. - Chai Wah Wu, Feb 27 2016

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..1500
• Index entries for sequences related to sums of squares

Programs

Mathematica

nn = 7250; 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, ?(# >= 4 &)]] (* _T. D. Noe, Apr 07 2011 *)