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

0,4

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 0..40319

Index entries for sequences related to factorial numbers

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)

Example

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

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 *)

Prog

(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

Crossrefs

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

Cf. A000142, A076934, A329379.

Cf. also A328478.

Sequence in context: A336898 A300330 A328478 * A147088 A346468 A340083

Adjacent sequences: A093408 A093409 A093410 * A093412 A093413 A093414

Keyword

easy,nonn

Author

Amarnath Murthy, Mar 30 2004

Extensions

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

Definition further clarified by Antti Karttunen, May 18 2021

Status

approved