A376427 The number of distinct values of x+y+z+w (mod n) when x*y*z*w = 1 (mod n)

1, 1, 3, 1, 5, 3, 7, 2, 5, 5, 11, 3, 13, 7, 15, 4, 17, 5, 19, 5, 21, 11, 23, 6, 25, 13, 15, 7, 29, 15, 31, 8, 33, 17, 35, 5, 37, 19, 39, 10, 41, 21, 43, 11, 25, 23, 47, 12, 49, 25, 51, 13, 53, 15, 55, 14, 57, 29, 59, 15, 61, 31, 35, 16, 65, 33, 67, 17, 69, 35, 71, 10, 73, 37, 75, 19, 77, 39, 79, 20, 45, 41, 83, 21, 85, 43, 87, 22, 89, 25

Offset

1,3

Comments

The values of n for which a(n) = n seem to agree with A325128. But I have no proof.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1688

Maple

a:=proc(n)
local x, y, z, w, N;
N:={};
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) mod n = 1 mod n then N:=N union {(x+y+z+w) mod n}; fi;
   od:
  od:
 od:
od:
nops(N);
end:

Prog

(Python)
def A376427(n):
    s = set()
    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):
                try:
                    s.add((xyp+z+pow(xy*z%n, -1, n))%n)
                except:
                    continue
    return len(s) # Chai Wah Wu, Sep 23 2024

Crossrefs

Cf. A376296, A376183, A180783.

Sequence in context: A318060 A336652 A136655 * A060819 A318661 A089654

Adjacent sequences: A376424 A376425 A376426 * A376428 A376429 A376430

Keyword

nonn

Author

W. Edwin Clark, Sep 22 2024

Status

approved