A025313 Numbers that are the sum of 2 distinct nonzero squares in 3 or more ways.

325, 425, 650, 725, 845, 850, 925, 1025, 1105, 1300, 1325, 1445, 1450, 1525, 1625, 1690, 1700, 1825, 1850, 1885, 2050, 2125, 2210, 2225, 2405, 2425, 2465, 2525, 2600, 2650, 2665, 2725, 2825, 2873, 2890, 2900, 2925, 3050, 3125, 3145, 3250, 3380, 3400

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Sequence contains no primes (A000040) and no semiprimes (A001358). - Zak Seidov, Apr 07 2011

Sequences A025294 and A025313 are different. For example 1250 is not in A025313. A025294(9) = 1250 = 35^2 + 5^2 = 31^2 + 17^2 = 25^2 + 25^2 (not distinct squares). - Vaclav Kotesovec, Feb 27 2016

Numbers in A025294 but not in A025313 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^4 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^4 = 1250 is the smallest term in A025294 that is not in A025313. - Chai Wah Wu, Feb 27 2016

Examples

			325 = 1^2+18^2 = 6^2+17^2 = 10^2+15^2. [Zak Seidov, Apr 07 2011]
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..5386
• Index entries for sequences related to sums of squares

Programs

Mathematica

nn = 3400; 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, ?(# >= 3 &)]] (* _T. D. Noe, Apr 07 2011 *)