A328318 Number of nonzero digits in representation of A328316(n) in primorial base; Number of distinct prime factors in A328316(1+n).

0, 1, 1, 2, 1, 2, 1, 3, 5, 16, 104, 7447

Offset: 0

Author

Antti Karttunen, Oct 14 2019

Keywords

• nonn
• base
• hard
• more

Links

• Index entries for sequences related to primorial base

Crossrefs

Cf. A001221, A267263, A276086, A328316, A328317, A328319.

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328316(n) = if(!n,0,A276086(A328316(n-1)));
A267263(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += !!d; n = (n-d)/p; p = nextprime(1+p)); (s); };
A328318(n) = A267263(A328316(n));
\\ Or alternatively, more slowly as:
A328318(n) = omega(A328316(1+n));

Formula

a(n) = A267263(A328316(n)).

a(n) = A001221(A328316(1+n)).