A049046 Number of k >= 1 with k! == 1 (mod n).

0, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 4, 1, 2, 1, 1, 1, 5, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 4, 1, 5, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 1, 3, 1, 1

Offset

1,5

Comments

The first occurrences for 0..10 are 1, 2, 5, 29, 17, 23, 199, 619, 3313, 4093, 3011, ... (see A049050). - Antti Karttunen, Oct 01 2018

Links

Antti Karttunen, Table of n, a(n) for n = 1..12021

Example

From Antti Karttunen, Oct 01 2018: (Start)
a(1) = 0 because 1 divides all factorial numbers (A000142): 1, 2, 6, 24, ... and thus there are no cases where the remainder would be 1.
a(3) = 1 as (1! mod 3) = 1, (2! mod 3) = 2 and for 3! and larger factorials the remainder is always 0. Thus there is exactly one case where the remainder is one.
a(5) = 2 as (1! mod 5) = 1, (2! mod 5) = 2, (3! mod 5) = 1, (4! mod 5) = 5, (5! mod 5) = 0, and so on ever after for larger factorials.
(End)

Mathematica

Table[Length[Select[Range[100], Mod[#!, n] == 1 &]], {n, 1, 100}] (* G. C. Greubel, Oct 08 2018 *)

Prog

(PARI) A049046(n) = { my(s=0, r, k=1); while((r=(k! % n))>0, s += (1==r); k++); (s); }; \\ Antti Karttunen, Oct 01 2018

Crossrefs

Cf. A000142, A002034, A071710, A038203, A049050.

Sequence in context: A131017 A244227 A214713 * A227945 A003647 A353352

Adjacent sequences: A049043 A049044 A049045 * A049047 A049048 A049049

Keyword

nonn

Author

David W. Wilson

Extensions

Term a(1) corrected and the definition clarified by Antti Karttunen, Oct 01 2018

Definition further edited by Antti Karttunen, Oct 06 2018, based on feedback from David W. Wilson

Status

approved