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A334382 Least k whose set of divisors contains exactly n Pythagorean triples, or 0 if no such k exists.

%I A334382 #17 Apr 27 2020 06:11:43
%S A334382 60,120,240,360,960,720,3840,1440,2160,2880,8160,3600,69360,8400,8640,
%T A334382 7200,32640,9360,16800,14400,34560,24480,130560,18720,77760,54600,
%U A334382 28080,25200,67200,37440,11045580,61200,73440,97920,294000,46800,65520,50400,268800,109200
%N A334382 Least k whose set of divisors contains exactly n Pythagorean triples, or 0 if no such k exists.
%C A334382 This is a subsequence of A169823: a(n) == 0 (mod 60) because one side of every Pythagorean triple is divisible by 3, another by 4, and another by 5. The smallest and best-known Pythagorean triple is (a, b, c) = (3, 4, 5).
%H A334382 Giovanni Resta, <a href="/A334382/b334382.txt">Table of n, a(n) for n = 1..450</a>
%e A334382 a(3) = 240 because the set of divisors {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240} contains 3 Pythagorean triples: (3, 4, 5), (6, 8, 10) and (12, 16, 20). The first triple is primitive.
%p A334382 with(numtheory):
%p A334382 for n from 1 to 52 do :
%p A334382 ii:=0:
%p A334382 for k from 60 by 60 to 10^8 while(ii=0) do:
%p A334382    d:=divisors(k):n0:=nops(d):it:=0:
%p A334382     for i from 1 to n0-1 do:
%p A334382      for j from i+1 to n0-2 do :
%p A334382       for m from i+2 to n0 do:
%p A334382        if d[i]^2 + d[j]^2 = d[m]^2
%p A334382         then
%p A334382         it:=it+1:
%p A334382         else
%p A334382        fi:
%p A334382       od:
%p A334382      od:
%p A334382     od:
%p A334382     if it = n
%p A334382      then
%p A334382      ii:=1: printf (`%d %d \n`,n,k):
%p A334382      else
%p A334382     fi:
%p A334382 od:
%p A334382 od:
%Y A334382 Cf. A103605, A103606, A169823, A334080.
%K A334382 nonn,hard
%O A334382 1,1
%A A334382 _Michel Lagneau_, Apr 26 2020
%E A334382 a(31) from _Giovanni Resta_, Apr 27 2020