A193511 -id:A193511 - cp's OEIS frontend

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

Michel Lagneau, Jul 29 2011

nonn

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

a(1) = 0 by convention.

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

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

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

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

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

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

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

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

A290080 a(1) = 0; for n > 1, a(n) = sigma(bigomega(n)).

Original entry on oeis.org

0, 1, 1, 3, 1, 3, 1, 4, 3, 3, 1, 4, 1, 3, 3, 7, 1, 4, 1, 4, 3, 3, 1, 7, 3, 3, 4, 4, 1, 4, 1, 6, 3, 3, 3, 7, 1, 3, 3, 7, 1, 4, 1, 4, 4, 3, 1, 6, 3, 4, 3, 4, 1, 7, 3, 7, 3, 3, 1, 7, 1, 3, 4, 12, 3, 4, 1, 4, 3, 4, 1, 6, 1, 3, 4, 4, 3, 4, 1, 6, 7, 3, 1, 7, 3, 3, 3, 7, 1, 7, 3, 4, 3, 3, 3, 12, 1, 4, 4, 7, 1, 4, 1, 7, 4

Offset: 1

Antti Karttunen, Jul 23 2017

nonn

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

Cf. A000203, A001222, A193511, A193512.

Differs from A289617 for the first time at n=32, where a(n) = 6, while A289617(32) = 8.

(define (A290080 n) (if (= 1 n) 0 (A000203 (A001222 n))))

a(1) = 0; for n > 1, a(n) = A000203(A001222(n)).

a(n) = A193511(n) + A193512(n).

cp's OEIS Frontend

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

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