A376318 The number of distinct values of x+y+z (mod n) when x*y*z = 1 (mod n).

1, 1, 2, 1, 4, 2, 7, 2, 4, 4, 11, 2, 13, 7, 8, 3, 17, 4, 19, 4, 14, 11, 23, 4, 20, 13, 11, 7, 29, 8, 31, 6, 22, 17, 28, 4, 37, 19, 26, 8, 41, 14, 43, 11, 16, 23, 47, 6, 49, 20, 34, 13, 53, 11, 44, 14, 38, 29, 59, 8, 61, 31, 28, 11, 52, 22, 67, 17, 46, 28, 71, 8, 73, 37, 40, 19, 77, 26

Offset

1,3

Comments

The values of n for which a(n) = n seem to be A007775, but I have no proof of this.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..30000

Charles R Greathouse IV, Program for computing terms (C with PARI)

Maple

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

Prog

(Python)
def A376318(n):
    s = set()
    for x in range(n):
        for y in range(x, n):
            try:
                s.add((x+y+pow(x*y%n, -1, n))%n)
            except:
                continue
    return len(s) # Chai Wah Wu, Sep 23 2024
(PARI) a(n)=my(v=vectorsmall(n)); for(x=1, n, if(gcd(x, n)>1, next); for(y=1, x, if(gcd(y, n)>1, next); my(z=1/Mod(x*y, n)); v[lift(x+y+z)+1]=1)); sum(i=1, n, v[i]) \\ Charles R Greathouse IV, Sep 23 2024

Crossrefs

Cf. A007775, A376296, A376183, A180783, A376427.

Sequence in context: A143375 A339418 A074364 * A256610 A276055 A252866

Adjacent sequences: A376315 A376316 A376317 * A376319 A376320 A376321

Keyword

nonn,mult

Author

W. Edwin Clark, Sep 22 2024

Status

approved