A328581 Product of nonzero digits in primorial base expansion of n.

1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 4, 4, 3, 3, 3, 3, 6, 6, 4, 4, 4, 4, 8, 8, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 4, 4, 3, 3, 3, 3, 6, 6, 4, 4, 4, 4, 8, 8, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 8, 8, 6, 6, 6, 6, 12, 12, 8, 8, 8, 8, 16, 16, 3, 3, 3, 3, 6, 6, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6

Offset: 0

Author

Antti Karttunen, Oct 21 2019

Keywords

• nonn
• base

Comments

a(0) = 1 as an empty product.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..32768
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A005361, A049345, A276086, A324655, A328582.

Cf. A276156 (positions of 1's).

Cf. also A227153 (an analogous sequence).

Programs

Mathematica

a[n_] := Module[{k = n, p = 2, s = 1, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, If[r > 0, s *= r]; p = NextPrime[p]]; s]; Array[a, 100, 0] (* Amiram Eldar, Mar 06 2024 *)

PARI

A328581(n) = { my(m=1, p=2); while(n, if(n%p, m *= (n%p)); n = n\p; p = nextprime(1+p)); (m); };

Formula

a(n) = A005361(A276086(n)).