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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to factorial numbers

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).

Mathematica

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

Prog

(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));

Crossrefs

Cf. A002034, A072480, A345932, A345933.

Sequence in context: A346099 A345941 A088492 * A025492 A322445 A276035

Adjacent sequences: A345928 A345929 A345930 * A345932 A345933 A345934

Keyword

nonn

Author

Antti Karttunen, Jul 01 2021

Status

approved