A353509 a(n) = A353379(n) - A001222(n).

0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 0, 4, 0, 4, 2, 2, 0, 7, 0, 2, 0, 4, 0, 9, 0, 0, 2, 2, 2, 8, 0, 2, 2, 7, 0, 9, 0, 4, 4, 2, 0, 10, 0, 4, 2, 4, 0, 7, 2, 7, 2, 2, 0, 16, 0, 2, 4, 0, 2, 9, 0, 4, 2, 9, 0, 14, 0, 2, 4, 4, 2, 9, 0, 10, 0, 2, 0, 16, 2, 2, 2, 7, 0, 16, 2, 4, 2, 2, 2, 15, 0, 4, 4, 8, 0, 9

Offset: 1

Author

Antti Karttunen, Apr 29 2022

Keywords

• nonn

Comments

The difference of A258851 (primepi-based arithmetic derivative) and A056239 (sum of prime indices with multiplicity) applied to A181819, the prime shadow of n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A001222, A056239, A181819, A258851, A278510, A353379.

Programs

PARI

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
A353509(n) = (A258851(A181819(n))-bigomega(n));

Formula

a(n) = A278510(A181819(n)) = A353379(n) - A001222(n).