

A334382


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


1



60, 120, 240, 360, 960, 720, 3840, 1440, 2160, 2880, 8160, 3600, 69360, 8400, 8640, 7200, 32640, 9360, 16800, 14400, 34560, 24480, 130560, 18720, 77760, 54600, 28080, 25200, 67200, 37440, 11045580, 61200, 73440, 97920, 294000, 46800, 65520, 50400, 268800, 109200
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OFFSET

1,1


COMMENTS

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 bestknown Pythagorean triple is (a, b, c) = (3, 4, 5).


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..450


EXAMPLE

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.


MAPLE

with(numtheory):
for n from 1 to 52 do :
ii:=0:
for k from 60 by 60 to 10^8 while(ii=0) do:
d:=divisors(k):n0:=nops(d):it:=0:
for i from 1 to n01 do:
for j from i+1 to n02 do :
for m from i+2 to n0 do:
if d[i]^2 + d[j]^2 = d[m]^2
then
it:=it+1:
else
fi:
od:
od:
od:
if it = n
then
ii:=1: printf (`%d %d \n`, n, k):
else
fi:
od:
od:


CROSSREFS

Cf. A103605, A103606, A169823, A334080.
Sequence in context: A169823 A309842 A177871 * A337098 A252953 A309315
Adjacent sequences: A334379 A334380 A334381 * A334383 A334384 A334385


KEYWORD

nonn,hard


AUTHOR

Michel Lagneau, Apr 26 2020


EXTENSIONS

a(31) from Giovanni Resta, Apr 27 2020


STATUS

approved



