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

1,1

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 4k+3 and q is a prime of the form 4k+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

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 *)

Crossrefs

Cf. A025301. [From R. J. Mathar, Oct 23 2008]

Sequence in context: A069336 A296341 A025301 * A025293 A025311 A081429

Adjacent sequences: A025317 A025318 A025319 * A025321 A025322 A025323

Keyword

nonn

Author

David W. Wilson

Status

approved