A375004 Number of ordered primitive solutions (x,y,z,w) to x*y + x*z + x*w + y*z + y*w + z*w = n with x,y,z,w >= 1.
0, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 4, 6, 0, 4, 0, 12, 8, 0, 0, 16, 6, 12, 4, 12, 0, 16, 12, 24, 8, 0, 12, 34, 0, 24, 8, 30, 12, 16, 0, 36, 32, 24, 12, 32, 6, 36, 16, 36, 12, 40, 12, 72, 8, 0, 24, 64, 24, 48, 32, 30, 24, 56, 12, 72, 8, 48, 24, 70, 24, 60, 32, 54, 24, 40, 12, 120, 62, 24, 24, 76, 24, 96, 32
Offset: 1
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
Programs
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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+x*z+x*w+y*z+y*w+z*w==n)))));
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Python
from math import gcd from sympy import divisors, integer_nthroot def A375004(n): k = 0 for c in range(1,n-1): for d in divisors(c,generator=True): for x in range(1,d): y = d-x xy = x*y a = (c//d)**2 b = a-(n-c-xy<<2) if b>=0: q,r = integer_nthroot(b,2) if r: w = c//d+q>>1 z = c//d-w if 1<=w
>1 z = c//d-w if 1<=w Chai Wah Wu, Jul 27 2024