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A193512
a(n) = Sum of odd divisors of Omega(n), a(1) = 0.
3
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.
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 29 2011
EXTENSIONS
Description clarified, more terms from Antti Karttunen, Jul 23 2017
STATUS
approved