A093411 Divide n by the largest factorial that divides it and repeat until an odd number is reached, which will be the result; a(0) = 0.

0, 1, 1, 3, 1, 5, 1, 7, 1, 9, 5, 11, 1, 13, 7, 15, 1, 17, 3, 19, 5, 21, 11, 23, 1, 25, 13, 27, 7, 29, 5, 31, 1, 33, 17, 35, 1, 37, 19, 39, 5, 41, 7, 43, 11, 45, 23, 47, 1, 49, 25, 51, 13, 53, 9, 55, 7, 57, 29, 59, 5, 61, 31, 63, 1, 65, 11, 67, 17, 69, 35, 71, 3, 73, 37, 75, 19, 77, 13, 79

Offset: 0

Author

Amarnath Murthy, Mar 30 2004

Keywords

• easy
• nonn

Comments

a(n) is odd for all positive n>0; a(n) = n iff n is odd.

Examples

			a(18) = 3, 18/6 = 3. though 18/2 = 9.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..40319
• Index entries for sequences related to factorial numbers

Crossrefs

For bisection see A109375, for positions of ones, A344181.

Cf. A000142, A076934, A329379.

Cf. also A328478.

Programs

Mathematica

f[n_] := Block[{m = n, k = n}, While[k > 1, While[ IntegerQ[m/k! ], m = m/k! ]; k-- ]; m]; Table[ f[n], {n, 0, 79}] (* Robert G. Wilson v *)

PARI

A076934(n) = for(k=2, oo , if(n%k, return(n), n /= k));
A093411(n) = if(!n,n, if(n%2, n, A093411(A076934(n)))); \\ Antti Karttunen, May 18 2021

Formula

From Antti Karttunen, May 18 2021: (Start)

a(0) = 0, a(2n+1) = 2n+1, a(2n) = a(A076934(2n)).

a(n) = n / A329379(n).

(End)

Extensions

Edited, corrected and extended by Robert G. Wilson v, Aug 25 2005

Definition further clarified by Antti Karttunen, May 18 2021