login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A061142 Replace each prime factor of n by 2: a(n)=2^bigomega(n). 24
1, 2, 2, 4, 2, 4, 2, 8, 4, 4, 2, 8, 2, 4, 4, 16, 2, 8, 2, 8, 4, 4, 2, 16, 4, 4, 8, 8, 2, 8, 2, 32, 4, 4, 4, 16, 2, 4, 4, 16, 2, 8, 2, 8, 8, 4, 2, 32, 4, 8, 4, 8, 2, 16, 4, 16, 4, 4, 2, 16, 2, 4, 8, 64, 4, 8, 2, 8, 4, 8, 2, 32, 2, 4, 8, 8, 4, 8, 2, 32, 16, 4, 2, 16, 4, 4, 4, 16, 2, 16, 4, 8, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
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..10000

R. J. Mathar, Survey of Dirichlet series..., arXiv:1106.4038, 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

a(n) = A000079(A001222(n)), i.e., a(n)=2^bigomega(n). - Emeric Deutsch, Feb 13 2005

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

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 */

CROSSREFS

Cf. A001222, A000079, A123667.

Cf. A034444, A124508.

Sequence in context: A085191 A188581 A165872 * A278525 A226083 A182730

Adjacent sequences:  A061139 A061140 A061141 * A061143 A061144 A061145

KEYWORD

easy,nonn,mult

AUTHOR

Henry Bottomley, May 29 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 23 04:27 EDT 2017. Contains 283902 sequences.