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
Keywords
Examples
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)
Links
- Antti Karttunen, Table of n, a(n) for n = 1..12021
Programs
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Mathematica
Table[Length[Select[Range[100], Mod[#!, n] == 1 &]], {n, 1, 100}] (* G. C. Greubel, Oct 08 2018 *) -
PARI
A049046(n) = { my(s=0, r, k=1); while((r=(k! % n))>0, s += (1==r); k++); (s); }; \\ Antti Karttunen, Oct 01 2018
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
Comments