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%I #17 Apr 27 2020 06:11:43
%S 60,120,240,360,960,720,3840,1440,2160,2880,8160,3600,69360,8400,8640,
%T 7200,32640,9360,16800,14400,34560,24480,130560,18720,77760,54600,
%U 28080,25200,67200,37440,11045580,61200,73440,97920,294000,46800,65520,50400,268800,109200
%N Least k whose set of divisors contains exactly n Pythagorean triples, or 0 if no such k exists.
%C 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 Giovanni Resta, <a href="/A334382/b334382.txt">Table of n, a(n) for n = 1..450</a>
%e 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 with(numtheory):
%p for n from 1 to 52 do :
%p ii:=0:
%p for k from 60 by 60 to 10^8 while(ii=0) do:
%p d:=divisors(k):n0:=nops(d):it:=0:
%p for i from 1 to n0-1 do:
%p for j from i+1 to n0-2 do :
%p for m from i+2 to n0 do:
%p if d[i]^2 + d[j]^2 = d[m]^2
%p then
%p it:=it+1:
%p else
%p fi:
%p od:
%p od:
%p od:
%p if it = n
%p then
%p ii:=1: printf (`%d %d \n`,n,k):
%p else
%p fi:
%p od:
%p od:
%Y Cf. A103605, A103606, A169823, A334080.
%K nonn,hard
%O 1,1
%A _Michel Lagneau_, Apr 26 2020
%E a(31) from _Giovanni Resta_, Apr 27 2020
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