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A025318 Numbers that are the sum of 2 distinct nonzero squares in 8 or more ways. 5
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, 107185, 110500, 111605, 112625, 114985 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A025299. But sequences A025318 and A025299 are different. 2*5^14 = 12207031250 = 7285^2 + 110245^2 = 15625^2 + 109375^2 = 23875^2 + 107875^2 = 45625^2 + 100625^2 = 53125^2 + 96875^2 = 60319^2 + 92567^2 = 71975^2 + 83825^2 = 78125^2 + 78125^2 (not distinct squares) is not in A025318. - Vaclav Kotesovec, Feb 27 2016

Numbers in A025299 but not in A025318 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q_1^14 or of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q_1^2*q_2^4 where p_i are distinct primes of the form 4k+3 and q_1, q_2 are distinct primes of the form 4k+1.  Thus 2*5^4*13^2 = 211250 is the smallest term in A025299 that is not in A025318. - 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 = 114985; 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, _?(# >= 8 &)]] (* T. D. Noe, Apr 07 2011 *)

CROSSREFS

Sequence in context: A025298 A025317 A025299 * A025291 A025309 A097244

Adjacent sequences:  A025315 A025316 A025317 * A025319 A025320 A025321

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)