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

1,2

Comments

Largest m! which divides n.

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.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Cf. also A053589.

Sequence in context: A356158 A071416 A053589 * A225821 A368777 A113766

Adjacent sequences: A055767 A055768 A055769 * A055771 A055772 A055773

Keyword

nonn,easy

Author

Labos Elemer, Jul 12 2000

Extensions

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

Status

approved