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

1,4

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 * A347459 A064575 A180251

Adjacent sequences: A069261 A069262 A069263 * A069265 A069266 A069267

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 19 2002

Status

approved