A376296 The number of solutions x<=y<=z<=w in Z/(n) of the equation x+y+z+w = x*y*z*w.

1, 2, 6, 7, 14, 18, 27, 34, 51, 59, 91, 96, 134, 136, 208, 203, 285, 261, 385, 373, 493, 487, 650, 616, 818, 750, 949, 947, 1240, 1146, 1517, 1397, 1766, 1662, 2089, 1824, 2443, 2309, 2723, 2638, 3311, 2977, 3801, 3482, 4024, 3962, 4900, 4382, 5525, 5023, 6078

Offset: 1

Author

W. Edwin Clark, Sep 19 2024

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1351

Crossrefs

Cf. A376183, A180783.

Programs

Maple

a:=proc(n)
local x,y,z,w,N;
N:=0:
for x from 0 to n-1 do
 for y from x to n-1 do
  for z from y to n-1 do
   for w from z to n-1 do
    if (x+y+z+w-x*y*z*w) mod n = 0 then N:=N + 1; fi;
   od:
  od:
 od:
od:
N;
end:

Python

def A376296(n):
    c = 0
    for x in range(n):
        for y in range(x,n):
            xy,xyp = x*y%n,(x+y)%n
            for z in range(y,n):
                xyz, xyzp = xy*z%n-1,(xyp+z)%n
                c += sum(not (xyz*w-xyzp)%n for w in range(z,n))
    return c # Chai Wah Wu, Sep 19 2024