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A373042 a(n) is the number of 3-element subsets {x,y,z} of {1,...,n} such that x*y*z is a square.

%I A373042 #11 May 30 2024 22:22:08
%S A373042 0,0,0,1,1,4,6,8,8,13,13,15,18,23,23,35,35,44,47,50,50,62,74,77,96,
%T A373042 107,107,117,117,145,150,154,160,182,182,186,191,211,211,223,223,236,
%U A373042 263,267,267,304,338,390,396,412,412,457,466,492,499,504,504,536,536,541,575
%N A373042 a(n) is the number of 3-element subsets {x,y,z} of {1,...,n} such that x*y*z is a square.
%H A373042 Hugo Pfoertner, <a href="/A373042/b373042.txt">Table of n, a(n) for n = 3..2000</a>
%e A373042 a(6) = a(7) = 1: 2*3*6 = 36.
%e A373042 a(8) = 4: 1*2*8 = 16, 2*3*6 = 36, 2*4*8 = 64, 3*6*8 = 144.
%o A373042 (PARI) a(n) = my(k=0); forsubset([n,3], s, if(issquare(vecprod(Vec(s))), k++)); k
%o A373042 (Python)
%o A373042 from math import prod
%o A373042 from itertools import combinations
%o A373042 from sympy.ntheory.primetest import is_square
%o A373042 def A373042(n): return sum(1 for p in combinations(range(1,n+1),3) if is_square(prod(p))) # _Chai Wah Wu_, May 30 2024
%Y A373042 Cf. A372306, A373043.
%K A373042 nonn
%O A373042 3,6
%A A373042 _Hugo Pfoertner_, May 25 2024