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%I #23 Nov 04 2020 14:37:29
%S 20,90,272,468,650,1332,2450,2900,3600,4160,6642,7650,10100,10388,
%T 14762,16400,20880,25578,27540,28730,38612,42048,50850,50960,54900,
%U 65792,83810,90650,98100,116948,125712,130682,141570,142400,149940,160400,194922,206100,214650
%N Primitive numbers that are the sum of the squares of two of their distinct divisors.
%C If m is a term of A337988 then k^2*m is another term for any k in N*; so, there exist primitive terms m as 20, 90, 272,... in the sense that m' is not a term for any m' = m/k^2, k>1.
%H Chai Wah Wu, <a href="/A338485/b338485.txt">Table of n, a(n) for n = 1..637</a>
%e 20 = 2^2 + 4^2 and there is no k>1 such that 20/k^2 is another term, so 20 is in the sequence.
%e 90 = 3^2 + 9^2 and there is no k>1 such that 90/k^2 is another term, so 90 is in the sequence.
%e 468 = 12^2 + 18^2 and there is no k>1 such that 468/k^2 is another term, so 468 is in the sequence.
%t sumdivQ[n_] := AnyTrue[Most @ Divisors[n], (s = n - #^2) > 0 && s != n/2 && IntegerQ@Sqrt[s] && Divisible[n, Sqrt[s]] &]; s = Select[Range[200000], sumdivQ]; seq = {s[[1]]}; Do[If[! AnyTrue[s[[1 ;; k - 1]], IntegerQ@Sqrt[s[[k]]/#] &], AppendTo[seq, s[[k]]]], {k, 2, Length[s]}]; seq (* _Amiram Eldar_, Oct 31 2020 *)
%o (PARI) isok(m) = {my(d=divisors(m)); for (i=2, #d, for (j=1, i-1, if (d[i]^2+d[j]^2 == m, return (1)); ); ); } \\ A337988
%o isprim(x, vp) = {for (i=1, #vp, my(y = x/vp[i]); if ((denominator(y)==1) && issquare(y), return (0));); return(1);}
%o lista(nn) = {my(vp = []); for (n=1, nn, if (isok(n) && isprim(n, vp), vp = concat(vp, n));); vp;} \\ _Michel Marcus_, Oct 30 2020
%Y Subsequence of A337988.
%Y A071253 is a subsequence.
%K nonn
%O 1,1
%A _Bernard Schott_, Oct 30 2020
%E More terms from _Michel Marcus_, Oct 30 2020
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