VOOZH about

URL: https://oeis.org/A069264

⇱ A069264 - OEIS

login
A069264
Inverse Moebius transform of bigomega(n).
5
0, 1, 1, 3, 1, 4, 1, 6, 3, 4, 1, 9, 1, 4, 4, 10, 1, 9, 1, 9, 4, 4, 1, 16, 3, 4, 6, 9, 1, 12, 1, 15, 4, 4, 4, 18, 1, 4, 4, 16, 1, 12, 1, 9, 9, 4, 1, 25, 3, 9, 4, 9, 1, 16, 4, 16, 4, 4, 1, 24, 1, 4, 9, 21, 4, 12, 1, 9, 4, 12, 1, 30, 1, 4, 9, 9, 4, 12, 1, 25, 10, 4, 1, 24, 4, 4, 4, 16, 1, 24, 4, 9, 4, 4
OFFSET
1,4
COMMENTS
a(n) is the total number of prime factors (counted with multiplicity) over all the divisors of n. - Geoffrey Critzer, Feb 03 2015
LINKS
FORMULA
a(n) = tau(n)*bigomega(n)/2. - Vladeta Jovovic, Jan 25 2004
G.f.: Sum_{k>=1} bigomega(k)*x^k/(1 - x^k). - Ilya Gutkovskiy, Feb 19 2017
EXAMPLE
a(12)=9 because the divisors of 12 are: 1,2,3,4,6,12 and the number (with multiplicity) of prime factors of these divisors is: 0+1+1+2+2+3=9. - Geoffrey Critzer, Feb 03 2015
MATHEMATICA
Table[Sum[PrimeOmega[d], {d, Divisors[n]}], {n, 1, 94}] (* Geoffrey Critzer, Feb 03 2015 *)
PROG
(PARI) for(n=1, 120, print1(sumdiv(n, d, bigomega(d)), ", "))
CROSSREFS
Sequence in context: A016474 A389026 A332678 * A347459 A064575 A180251
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 19 2002
STATUS
approved