A193512 a(n) = Sum of odd divisors of Omega(n), a(1) = 0.

0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 1, 1, 4, 1, 4, 1, 1, 1, 1, 1, 1, 4, 4, 1, 4, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 4, 4, 1, 1, 6, 1, 4, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 1, 4, 1, 4, 1, 4, 1, 6, 1, 1, 4, 4, 1, 4, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 4, 1, 4, 4, 1, 1, 4, 1, 1, 4

Offset

1,8

Comments

Omega = A001222 is the number of prime divisors of the argument, counted with multiplicity.

a(1) = 0 by convention.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

Formula

a(1) = 0, for n > 1, a(n) = A000593(A001222(n)).

a(n) + A193511(n) = A290080(n). - Antti Karttunen, Jul 23 2017

Example

a(8) = 4 because Omega(8) = 3 and the sum of the 2 odd divisors {1, 3} is 4.

Mathematica

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

Prog

(PARI)
A000593(n) = sigma(n>>valuation(n, 2)); \\ This function from Charles R Greathouse IV, Sep 09 2014
A193512(n) = if(1==n, 0, A000593(bigomega(n))); \\ Antti Karttunen, Jul 23 2017

Crossrefs

Cf. A000593, A001222, A193509, A193511, A290080.

Sequence in context: A332847 A245501 A247026 * A366524 A366523 A365635

Adjacent sequences: A193509 A193510 A193511 * A193513 A193514 A193515

Keyword

nonn

Author

Michel Lagneau, Jul 29 2011

Extensions

Description clarified, more terms from Antti Karttunen, Jul 23 2017

Status

approved