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 best-known 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 n0-1 do:
for j from i+1 to n0-2 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
KEYWORD
nonn,hard
AUTHOR
Michel Lagneau, Apr 26 2020
EXTENSIONS
a(31) from Giovanni Resta, Apr 27 2020
STATUS
approved