A025320 Numbers that are the sum of 2 distinct nonzero squares in 10 or more ways.

138125, 160225, 204425, 226525, 235625, 276250, 292825, 300625, 308125, 320450, 333125, 337025, 348725, 359125, 386425, 393125, 403325, 408850, 416585, 430625, 435625, 453050, 456025, 469625, 471250, 491725, 493025, 495625, 499525, 505325

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Subsequence of A025301. But sequences A025320 and A025301 are different. 2*5^18 = 7629394531250 = 182125^2 + 2756125^2 = 390625^2 + 2734375^2 = 596875^2 + 2696875^2 = 799687^2 + 2643841^2 = 946555^2 + 2594885^2 = 1140625^2 + 2515625^2 = 1328125^2 + 2421875^2 = 1507975^2 + 2314175^2 = 1799375^2 + 2095625^2 = 1953125^2 + 1953125^2 (not distinct squares) is not in A025320. - Vaclav Kotesovec, Feb 27 2016

Numbers in A025301 but not in A025320 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^18 where p_i are primes of the form 4*k+3 and q is a prime of the form 4*k+1. Thus 2*5^18 is the smallest term in A025301 that is not in A025320. - 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

Crossrefs

Cf. A025301. - R. J. Mathar, Oct 23 2008

Programs

Mathematica

nn = 505325; 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, ?(# >= 10 &)]] (* _T. D. Noe, Apr 07 2011 *)