A227154 Product of digits+1 of n in factorial base.

1, 2, 2, 4, 3, 6, 2, 4, 4, 8, 6, 12, 3, 6, 6, 12, 9, 18, 4, 8, 8, 16, 12, 24, 2, 4, 4, 8, 6, 12, 4, 8, 8, 16, 12, 24, 6, 12, 12, 24, 18, 36, 8, 16, 16, 32, 24, 48, 3, 6, 6, 12, 9, 18, 6, 12, 12, 24, 18, 36, 9, 18, 18, 36, 27, 54, 12, 24, 24, 48, 36, 72, 4, 8, 8

Offset

0,2

Links

Antti Karttunen, Table of n, a(n) for n = 0..5040 (corrected by Ray Chandler, Jan 19 2019)

Tyler Ball, Joanne Beckford, Paul Dalenberg, Tom Edgar, and Tina Rajabi, Some Combinatorics of Factorial Base Representations, J. Int. Seq., Vol. 23 (2020), Article 20.3.3.

Index entries for sequences related to factorial base representation.

Example

5 has factorial base representation A007623(5) = "21" (as 2*2 + 1*1 = 5). Adding one to these digits and multiplying, we get 3*2 = 6, thus a(5)=6.

Mathematica

a[n_] := Module[{k = n, m = 2, r, p = 1}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, p *= (r+1); m++]; p]; Array[a, 100, 0] (* Amiram Eldar, Feb 13 2024 *)

Prog

(MIT/GNU Scheme):
(define (A227154 n) (apply * (map 1+ (n->factbase n))))
(define (n->factbase n) (let loop ((n n) (fex (if (zero? n) (list 0) (list))) (i 2)) (cond ((zero? n) fex) (else (loop (floor->exact (/ n i)) (cons (modulo n i) fex) (1+ i))))))
(PARI) a(n)=my(b=2, t=1); while(n, t *= n%b + 1; n \= b; b++); t \\ Charles R Greathouse IV, Jun 06 2017

Crossrefs

Cf. A007623, A208575, A227153.

Sequence in context: A241450 A189675 A248746 * A324655 A275735 A328835

Adjacent sequences: A227151 A227152 A227153 * A227155 A227156 A227157

Keyword

nonn,base

Author

Antti Karttunen, Jul 04 2013

Extensions

a(0)=1 added by Tom Edgar, Jun 05 2017

Status

approved