A345931 a(n) = gcd(n, A002034(n)), where A002034(n) gives the smallest positive integer k such that n divides k!.

1, 2, 3, 4, 5, 3, 7, 4, 3, 5, 11, 4, 13, 7, 5, 2, 17, 6, 19, 5, 7, 11, 23, 4, 5, 13, 9, 7, 29, 5, 31, 8, 11, 17, 7, 6, 37, 19, 13, 5, 41, 7, 43, 11, 3, 23, 47, 6, 7, 10, 17, 13, 53, 9, 11, 7, 19, 29, 59, 5, 61, 31, 7, 8, 13, 11, 67, 17, 23, 7, 71, 6, 73, 37, 5, 19, 11, 13, 79, 2, 9, 41, 83, 7, 17, 43, 29, 11, 89

Offset: 1

Author

Antti Karttunen, Jul 01 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A002034, A072480, A345932, A345933.

Programs

Mathematica

Table[GCD[n,m=1;While[Mod[m!,n]!=0,m++];m],{n,100}] (* Giorgos Kalogeropoulos, Jul 02 2021 *)

PARI

A002034(n) = if(1==n,n,my(s=factor(n)[, 1], k=s[#s], f=Mod(k!, n)); while(f, f*=k++); (k)); \\ After code in A002034.
A345931(n) = gcd(n, A002034(n));

Formula

a(n) = gcd(n, A002034(n)) = gcd(n, A072480(n)) = gcd(A002034(n), A072480(n)).

a(n) = A002034(n) / A345932(n).

a(n) = n / A345933(n).