A193511 a(n) = Sum of even divisors of Omega(n), a(1) = 0.

0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 6, 0, 0, 0, 0, 2, 2, 0, 6, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 6, 0, 2, 2, 6, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 6, 2, 6, 2, 2, 0, 6, 0, 2, 0, 8, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0

Offset: 1

Author

Michel Lagneau, Jul 29 2011

Keywords

• nonn

Comments

Omega(n) = number of prime divisors of n counted with multiplicity : A001222 (also called bigomega(n)).

a(1) = 0 by convention.

Examples

			a(16) = 6 because Omega(16) = 4 and the sum of the even divisors of 4 {2, 4} is 6.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A001222, A146076, A193510, A193512, A290080.

Programs

Mathematica

Table[Total[Select[Divisors[PrimeOmega[n]], EvenQ[ # ]&]], {n, 58}]

PARI

A146076(n) = if(n%2, 0, 2*sigma(n/2)); \\ This function from Michel Marcus, Apr 01 2015
A193511(n) = if(1==n,0,A146076(bigomega(n))); \\ Antti Karttunen, Jul 23 2017

Formula

From Antti Karttunen, Jul 23 2017: (Start)

a(1) = 0, for n > 1, a(n) = A146076(A001222(n)).

a(n) + A193512(n) = A290080(n).

(End)

Extensions

Description clarified by Antti Karttunen, Jul 23 2017