A025319 Numbers that are the sum of 2 distinct nonzero squares in 9 or more ways.

71825, 93925, 122525, 138125, 143650, 156325, 160225, 173225, 187850, 204425, 209525, 223925, 226525, 235625, 244205, 245050, 257725, 267325, 273325, 276250, 287300, 292825, 296225, 300625, 308125, 308425, 312650, 320450, 333125, 337025

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Subsequence of A025300. But sequences A025319 and A025300 are different. 2*5^16 = 305175781250 = 36425^2 + 551225^2 = 78125^2 + 546875^2 = 119375^2 + 539375^2 = 189311^2 + 518977^2 = 228125^2 + 503125^2 = 265625^2 + 484375^2 = 301595^2 + 462835^2 = 359875^2 + 419125^2 = 390625^2 + 390625^2 (not distinct squares) is not in A025319. - Vaclav Kotesovec, Feb 27 2016

Numbers in A025300 but not in A025319 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^16 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^16 is the smallest term in A025300 that is not in A025319. - 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 = 337025; 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, ?(# >= 9 &)]] (* _T. D. Noe, Apr 07 2011 *)