A345933 a(n) = n / gcd(n, A002034(n)), where A002034(n) gives the smallest positive integer k such that n divides k!.

1, 1, 1, 1, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 8, 1, 3, 1, 4, 3, 2, 1, 6, 5, 2, 3, 4, 1, 6, 1, 4, 3, 2, 5, 6, 1, 2, 3, 8, 1, 6, 1, 4, 15, 2, 1, 8, 7, 5, 3, 4, 1, 6, 5, 8, 3, 2, 1, 12, 1, 2, 9, 8, 5, 6, 1, 4, 3, 10, 1, 12, 1, 2, 15, 4, 7, 6, 1, 40, 9, 2, 1, 12, 5, 2, 3, 8, 1, 15, 7, 4, 3, 2, 5, 12, 1, 7, 9, 10, 1, 6, 1, 8, 15

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences related to factorial numbers

Formula

a(n) = n / A345931(n) = n / gcd(n, A002034(n)).

Mathematica

Table[n/GCD[n, m=1; While[Mod[m!, n]!=0, m++]; m], {n, 100}] (* Giorgos Kalogeropoulos, Jul 03 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.
A345933(n) = (n/gcd(n, A002034(n)));

Crossrefs

Cf. A002034, A345931, A345932.

Sequence in context: A182110 A175328 A338776 * A198325 A293909 A002850

Adjacent sequences: A345930 A345931 A345932 * A345934 A345935 A345936

Keyword

nonn

Author

Antti Karttunen, Jul 01 2021

Status

approved