A025314 Numbers that are the sum of 2 distinct nonzero squares in 4 or more ways.

1105, 1625, 1885, 2125, 2210, 2405, 2465, 2665, 3145, 3250, 3445, 3485, 3625, 3770, 3965, 4225, 4250, 4420, 4505, 4625, 4745, 4810, 4930, 5125, 5185, 5330, 5365, 5525, 5785, 5945, 6205, 6290, 6305, 6409, 6500, 6565, 6625, 6890, 6970, 7085, 7225, 7250

Offset

1,1

Comments

Subsequence of A025295. But sequences A025295 and A025314 are different, A025295(346) = 31250 = 175^2 + 25^2 = 161^2 + 73^2 = 155^2 + 85^2 = 125^2 + 125^2 (not distinct squares) is not in A025314. - Vaclav Kotesovec, Feb 27 2016

Numbers in A025295 but not in A025314 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^6 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^6 = 31250 is the smallest term in A025295 that is not in A025314. - Chai Wah Wu, Feb 27 2016

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..1500

Index entries for sequences related to sums of squares

Mathematica

nn = 7250; 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, _?(# >= 4 &)]] (* T. D. Noe, Apr 07 2011 *)

Crossrefs

Sequence in context: A321870 A257759 A025295 * A025287 A025305 A052155

Adjacent sequences: A025311 A025312 A025313 * A025315 A025316 A025317

Keyword

nonn

Author

David W. Wilson

Status

approved