A353524 A003557 applied to the prime shadow of primorial base exp-function: a(n) = A003557(A181819(A276086(n))).

1, 1, 1, 2, 1, 1, 1, 2, 2, 4, 1, 2, 1, 1, 1, 2, 3, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 4, 1, 2, 2, 4, 4, 8, 2, 4, 1, 2, 2, 4, 3, 6, 1, 2, 2, 4, 1, 2, 1, 2, 2, 4, 1, 2, 1, 1, 1, 2, 3, 3, 1, 2, 2, 4, 3, 6, 3, 3, 3, 6, 9, 9, 1, 1, 1, 2, 3, 3, 1, 1, 1, 2, 3, 3, 1, 1, 1, 2, 1, 1, 1, 2, 2, 4, 1, 2, 1, 1, 1, 2

Offset: 0

Author

Antti Karttunen, Apr 30 2022

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..11550
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003557, A181819, A276086, A328835, A351944, A353576, A353577.

Programs

PARI

A003557(n) = (n/factorback(factorint(n)[, 1]));
A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A353524(n) = A003557(A181819(A276086(n)));

Formula

a(n) = A351944(A276086(n)) = A003557(A328835(n)) = A003557(A181819(A276086(n))).

For n > 0, a(n) = A353576(n) / A353577(n).