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

Author

Antti Karttunen, Jul 04 2013

Keywords

• nonn
• base

Examples

			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.
		

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.

Crossrefs

Cf. A007623, A208575, A227153.

Programs

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 *)

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

Extensions

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