A353575 Primepi based arithmetic derivative applied to the prime shadow of the primorial base exp-function: a(n) = A258851(A181819(A276086(n))).

0, 1, 1, 4, 2, 7, 1, 4, 4, 12, 7, 20, 2, 7, 7, 20, 12, 33, 3, 11, 11, 32, 19, 53, 4, 15, 15, 44, 26, 73, 1, 4, 4, 12, 7, 20, 4, 12, 12, 32, 20, 52, 7, 20, 20, 52, 33, 84, 11, 32, 32, 84, 53, 136, 15, 44, 44, 116, 73, 188, 2, 7, 7, 20, 12, 33, 7, 20, 20, 52, 33, 84, 12, 33, 33, 84, 54, 135, 19, 53, 53, 136, 87, 219

Offset: 0

Author

Antti Karttunen, Apr 29 2022

Keywords

• nonn
• base
• easy
• look

Links

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

Crossrefs

Cf. A181819, A258851, A276086, A328835, A353379.

Cf. also A342002, A353574 and A353576.

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
A258851(n) = (n*sum(i=1, #n=factor(n)~, n[2, i]*primepi(n[1, i])/n[1, i])); \\ From A258851
A353379(n) = A258851(A181819(n));
A353575(n) = A353379(A276086(n));

Formula

a(n) = A353379(A276086(n)) = A258851(A328835(n)).