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A374970 Number of ordered primitive solutions (x,y,z,w) to x*y + y*z + z*w + w*x = n with x,y,z,w >= 1.

%I A374970 #12 Jul 27 2024 04:56:19
%S A374970 0,0,0,1,0,4,0,6,4,8,0,22,0,12,16,22,0,36,0,42,24,20,0,76,16,24,32,62,
%T A374970 0,104,0,66,40,32,48,146,0,36,48,140,0,152,0,102,120,44,0,220,36,120,
%U A374970 64,122,0,196,80,204,72,56,0,380,0,60,176,178,96,248,0,162,88,280,0,444,0,72,208,182,120,296,0,396
%N A374970 Number of ordered primitive solutions (x,y,z,w) to x*y + y*z + z*w + w*x = n with x,y,z,w >= 1.
%C A374970 a(n) = 0 if and only if n = 1 or n is prime. - _Chai Wah Wu_, Jul 26 2024
%o A374970 (PARI) a(n) = sum(x=1, n, sum(y=1, n, sum(z=1, n, sum(w=1, n, (gcd([x, y, z, w])==1)*(x*y+y*z+z*w+w*x==n)))));
%o A374970 (Python)
%o A374970 from math import gcd
%o A374970 from sympy import divisors
%o A374970 def A374970(n): return sum(1 for d in divisors(n,generator=True) for x in range(1,d) for y in range(1,n//d) if gcd(x,y,d-x,n//d-y)==1) # _Chai Wah Wu_, Jul 26 2024
%Y A374970 Cf. A066958, A374969.
%K A374970 nonn
%O A374970 1,6
%A A374970 _Seiichi Manyama_, Jul 26 2024