A049047 Number of distinct factorial numbers congruent to 1 (mod prime(n)).

1, 1, 2, 2, 2, 2, 4, 2, 5, 3, 3, 2, 2, 2, 2, 4, 4, 5, 3, 3, 4, 2, 4, 4, 4, 2, 3, 3, 3, 2, 2, 2, 3, 4, 5, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2, 6, 3, 3, 3, 2, 5, 4, 2, 3, 2, 2, 2, 3, 3, 2, 3, 2, 4, 6, 2, 2, 5, 2, 2, 2, 2, 6, 2, 2, 3, 2, 4, 3, 5, 2, 3, 2, 3, 2, 5, 2, 5, 4, 5, 3, 5, 4, 3, 2, 4, 4, 2, 4, 2, 2, 3, 3, 2, 2, 4

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 5000 terms from Amiram Eldar)

Maple

a:= proc(n) option remember; local f, k, p, s; f, s, p:= 1$2, ithprime(n);
      for k from 2 to p-1 do f:= f*k mod p; if f=1 then s:=s+1 fi od: s
    end:
seq(a(n), n=1..105);  # Alois P. Heinz, Jun 01 2026

Mathematica

a[n_] := Module[{p = Prime[n]}, Count[Range[1, p-1], _?(Mod[#!, p] == 1 &)]]; Array[a, 100] (* Amiram Eldar, Aug 05 2025 *)

Prog

(PARI) a(n) = {my(p = prime(n)); sum(k = 1, p-1, k! % p == 1); } \\ Amiram Eldar, Aug 05 2025

Crossrefs

Cf. A000142.

Sequence in context: A003036 A089818 A067025 * A037088 A260722 A153436

Adjacent sequences: A049044 A049045 A049046 * A049048 A049049 A049050

Keyword

nonn,changed

Author

David W. Wilson

Status

approved