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

1,6

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

Formula

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

Prog

(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));

Crossrefs

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

Sequence in context: A328590 A219204 A338264 * A326067 A318879 A333783

Adjacent sequences: A353506 A353507 A353508 * A353510 A353511 A353512

Keyword

nonn

Author

Antti Karttunen, Apr 29 2022

Status

approved