A376183 The number of solutions x<=y<=z in Z/(n) of the equation x+y+z = x*y*z

1, 3, 2, 4, 7, 8, 10, 13, 13, 31, 24, 20, 37, 44, 38, 47, 59, 59, 66, 86, 53, 108, 96, 77, 137, 171, 100, 120, 159, 186, 170, 179, 135, 279, 230, 172, 253, 312, 220, 337, 307, 259, 322, 306, 331, 456, 384, 303, 369, 669, 366, 500, 503, 488, 588, 469, 409, 767, 600

Offset

1,2

Comments

Suggested by a discussion initiated by Keith F. Lynch on the MathFun mailing list Sept 8, 2024 about when sums and products of real numbers x,y,z are integers and later raising other similar questions.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..8450 (terms 1..2000 from Hugo Pfoertner)

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
   if (x+y+z-x*y*z) mod n = 0 then N:=N + 1; fi;
  od:
 od:
od:
N;
end:

Prog

(PARI) a(n) = sum(x=0, n-1, sum(y=x, n-1, sum(z=y, n-1, Mod(x+y+z-x*y*z, n)==0))); \\ Michel Marcus, Sep 15 2024
(Python)
def A376183(n):
    c = 0
    for x in range(n):
        for y in range(x, n):
            xy, xyp = x*y%n-1, (x+y)%n
            c += sum(not (xy*z-xyp)%n for z in range(y, n))
    return c # Chai Wah Wu, Sep 19 2024

Crossrefs

Sequence in context: A356957 A158441 A349368 * A102787 A014193 A128885

Adjacent sequences: A376180 A376181 A376182 * A376184 A376185 A376186

Keyword

nonn

Author

W. Edwin Clark, Sep 14 2024

Extensions

More terms from Hugo Pfoertner, Sep 15 2024

Status

approved