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Numbers that are the sum of 2 distinct nonzero squares in 9 or more ways.
5

%I #21 Feb 28 2016 03:06:21

%S 71825,93925,122525,138125,143650,156325,160225,173225,187850,204425,

%T 209525,223925,226525,235625,244205,245050,257725,267325,273325,

%U 276250,287300,292825,296225,300625,308125,308425,312650,320450,333125,337025

%N Numbers that are the sum of 2 distinct nonzero squares in 9 or more ways.

%C Subsequence of A025300. But sequences A025319 and A025300 are different. 2*5^16 = 305175781250 = 36425^2 + 551225^2 = 78125^2 + 546875^2 = 119375^2 + 539375^2 = 189311^2 + 518977^2 = 228125^2 + 503125^2 = 265625^2 + 484375^2 = 301595^2 + 462835^2 = 359875^2 + 419125^2 = 390625^2 + 390625^2 (not distinct squares) is not in A025319. - _Vaclav Kotesovec_, Feb 27 2016

%C Numbers in A025300 but not in A025319 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^16 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^16 is the smallest term in A025300 that is not in A025319. - _Chai Wah Wu_, Feb 27 2016

%H Chai Wah Wu, <a href="/A025319/b025319.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%t nn = 337025; 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, _?(# >= 9 &)]] (* _T. D. Noe_, Apr 07 2011 *)

%K nonn

%O 1,1

%A _David W. Wilson_