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

1,1

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

Links

Zak Seidov, Table of n, a(n) for n = 1..5386

Index entries for sequences related to sums of squares

Example

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

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 *)

Crossrefs

Sequence in context: A000443 A097101 A025294 * A025286 A025304 A351801

Adjacent sequences: A025310 A025311 A025312 * A025314 A025315 A025316

Keyword

nonn

Author

David W. Wilson

Status

approved