A069264 Inverse Moebius transform of bigomega(n).

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

Author

Benoit Cloitre, Apr 19 2002

Keywords

• easy
• nonn

Comments

a(n) is the total number of prime factors (counted with multiplicity) over all the divisors of n. - Geoffrey Critzer, Feb 03 2015

Examples

			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
		

Links

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

Crossrefs

Cf. A000005, A001222.

Programs

Mathematica

Table[Sum[PrimeOmega[d], {d, Divisors[n]}], {n, 1, 94}] (* Geoffrey Critzer, Feb 03 2015 *)

PARI

for(n=1,120,print1(sumdiv(n,d,bigomega(d)),","))

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