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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 (list; graph; refs; listen; history; text; internal format)
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

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

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

Cf. A000005, A001222.

Sequence in context: A309992 A016474 A332678 * A064575 A180251 A094119

Adjacent sequences:  A069261 A069262 A069263 * A069265 A069266 A069267

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Apr 19 2002

STATUS

approved

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Last modified February 24 18:32 EST 2021. Contains 341577 sequences. (Running on oeis4.)