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%I #38 Jun 24 2022 05:24:14
%S 1,5,65,325,1105,5525,27625,71825,138125,160225,801125,2082925,
%T 4005625,5928325,29641625,77068225,148208125,243061325,1215306625,
%U 3159797225,6076533125,12882250225,53716552825,64411251125,167469252925,322056255625,785817263725
%N Numbers that are expressible as the sum of 2 distinct positive squares in more ways than any smaller number.
%D Donald S. McDonald, Postings to sci.math newsgroup, Feb 21, 1995 and Dec 04, 1995.
%H Ray Chandler, <a href="/A052199/b052199.txt">Table of n, a(n) for n = 1..422</a>
%H Dirk Frettlöh, "Tile Orientations with Distinct Frequencies", Ch. 1.5 in <a href="https://doi.org/10.1017/9781139033862">Aperiodic Order</a>, Vol. 2: Crystallography and Almost Periodicity, 2017, see page 9.
%H Donald S. McDonald, <a href="http://www2.mat.dtu.dk/info/experiencing/ems-gallery/Gallery/Ideas/Ideas_Poster/ideas_poster_15.html">World Mathematical Year 2000 Poster Competition</a>
%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~twosquares.en.html">Two squares</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e 65 = 1^2 + 8^2 = 4^2 + 7^2, the smallest expressible in two ways, so 65 is a term.
%o (PARI)
%o c_old=-1;for(n=1,10000,c=0;for(i=1,floor(sqrt(n)),for(j=1,i-1,if(i^2+j^2==n,c+=1)));if(c>c_old,print1(n,", ");c_old=c)) - _Derek Orr_, Mar 15 2019
%Y Cf. A001983, A007511, A048610, A071383. Subsequence of A054994. Where records occur in A025441; corresponding number of ways is A060306.
%K nonn
%O 1,2
%A _Jud McCranie_, Jan 28 2000
%E More terms from _Randall L Rathbun_, Jan 18 2002
%E Edited by _Ray Chandler_, Jan 12 2012
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