A025317 Numbers that are the sum of 2 distinct nonzero squares in 7 or more ways.

27625, 32045, 40885, 45305, 47125, 55250, 58565, 60125, 61625, 64090, 66625, 67405, 69745, 71825, 77285, 78625, 80665, 81770, 86125, 87125, 90610, 91205, 93925, 94250, 98345, 98605, 99125, 99905, 101065, 105625, 107185, 110500, 111605, 112625

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Subsequence of A025298. But sequences A025317 and A025298 are different. 2*5^12 = 488281250 = 15625^2 + 15625^2 (not distinct squares) = 14395^2 + 16765^2 = 10625^2 + 19375^2 = 9125^2 + 20125^2 = 4775^2 + 21575^2 = 3125^2 + 21875^2 = 1457^2 + 22049^2 is not in A025317. - Vaclav Kotesovec, Feb 27 2016

Numbers in A025298 but not in A025317 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^12 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^12 is the smallest term in A025298 that is not in A025317. - 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 = 112625; 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, ?(# >= 7 &)]] (* _T. D. Noe, Apr 07 2011 *)