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.

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, 0, 104, 0, 66, 40, 32, 48, 146, 0, 36, 48, 140, 0, 152, 0, 102, 120, 44, 0, 220, 36, 120, 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

Offset: 1

Author

Seiichi Manyama, Jul 26 2024

Keywords

• nonn

Comments

a(n) = 0 if and only if n = 1 or n is prime. - Chai Wah Wu, Jul 26 2024

Crossrefs

Cf. A066958, A374969.

Programs

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)))));

Python

from math import gcd
from sympy import divisors
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