A055770 Largest factorial number which divides n.

1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 24, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 24, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 24, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 24, 1, 2, 1, 2, 1, 6

Offset: 1

Author

Labos Elemer, Jul 12 2000

Keywords

• nonn
• easy

Comments

Largest m! which divides n.

Examples

			3! = 6 divides 12, so a(12) = 6.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10080
• Tyler Ball, Joanne Beckford, Paul Dalenberg, Tom Edgar, Tina Rajabi, Some Combinatorics of Factorial Base Representations, J. Int. Seq., Vol. 23 (2020), Article 20.3.3.

Crossrefs

Cf. A000142, A055881 (values of the m's), A055926, A055874, A073575.

Cf. also A053589.

Programs

Mathematica

With[{rf=Reverse[Range[7]!]},Table[SelectFirst[rf,Divisible[n,#]&],{n,120}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 05 2017 *)

PARI

A055770(n) = { my(m=1, i=2); while(!(n%m), m *= i; i++); return(m/(i-1)); } \\ Antti Karttunen, Dec 19 2018

Formula

a(n) = A000142(A055881(n)). - Antti Karttunen, Dec 19 2018

Extensions

Name changed, old name moved to comments by Antti Karttunen, Dec 19 2018