

A025315


Numbers that are the sum of 2 distinct nonzero squares in 5 or more ways.


5



5525, 8125, 9425, 10625, 11050, 12025, 12325, 13325, 14365, 15725, 16250, 17225, 17425, 18125, 18785, 18850, 19825, 21125, 21250, 22100, 22525, 23125, 23725, 24050, 24505, 24650, 25625, 25925, 26650, 26825, 27625, 28730, 28925, 29725, 31025, 31265
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OFFSET

1,1


COMMENTS

Subsequence of A025296. But sequences A025315 and A025296 are different. 2*5^8 = 781250 = 625^2 + 625^2 (not distinct squares) = 425^2 + 775^2 = 365^2 + 805^2 = 191^2 + 863^2 = 125^2 + 875^2 is not in A025315.  Vaclav Kotesovec, Feb 27 2016
Numbers in A025296 but not in A025315 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q_1^8 or of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q_1^2*q_2^2 where p_i are primes of the form 4k+3 and q_1, q_2 are distinct primes of the form 4k+1. Thus 2*5^2*13^2 = 8450 is the smallest term in A025296 that is not in A025315.  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


MATHEMATICA

nn = 31265; 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, _?(# >= 5 &)]] (* T. D. Noe, Apr 07 2011 *)


CROSSREFS

Sequence in context: A250876 A165443 A025296 * A097103 A025297 A025316
Adjacent sequences: A025312 A025313 A025314 * A025316 A025317 A025318


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



