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 A334382 Least k whose set of divisors contains exactly n Pythagorean triples, or 0 if no such k exists. 1

%I

%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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Last modified April 20 20:26 EDT 2021. Contains 343137 sequences. (Running on oeis4.)