OFFSET
1,2
COMMENTS
The inverse Möbius transform of A162510. - R. J. Mathar, Feb 09 2011
LINKS
R. Zumkeller, Table of n, a(n) for n = 1..10005
R. J. Mathar, Survey of Dirichlet Series of Multiplicative Arithmetic Functions, arXiv:1106.4038 [math.NT], 2011-2012. See eq. (2.12).
FORMULA
a(n) = Sum_{d divides n} 2^(bigomega(d)-omega(d)) = Sum_{d divides n} 2^(A001222(d) - A001221(d)). - Benoit Cloitre, Apr 30 2002
Totally multiplicative with a(p) = 2. - Franklin T. Adams-Watters, Oct 04 2006
Dirichlet g.f.: Product_{p prime} 1/(1-2*p^(-s)). - Ralf Stephan, Mar 28 2015
Dirichlet g.f.: zeta(s)^2 * Product_{p prime} 1/(1 - 1/(p^s - 1)^2). - Vaclav Kotesovec, Mar 14 2023
EXAMPLE
a(100)=16 since 100=2*2*5*5 and so a(100)=2*2*2*2.
MAPLE
with(numtheory): seq(2^bigomega(n), n=1..95);
MATHEMATICA
Table[2^PrimeOmega[n], {n, 1, 95}] (* Jean-François Alcover, Jun 08 2013 *)
PROG
(PARI) a(n)=direuler(p=1, n, 1/(1-2*X))[n] /* Ralf Stephan, Mar 28 2015 */
(PARI) a(n) = 2^bigomega(n); \\ Michel Marcus, Aug 08 2017
CROSSREFS
KEYWORD
easy,nonn,mult
AUTHOR
Henry Bottomley, May 29 2001
STATUS
approved