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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A162510 Dirichlet inverse of A076479. 6
1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 1, 8, 1, 2, 1, 2, 1, 1, 1, 4, 2, 1, 4, 2, 1, 1, 1, 16, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 1, 8, 2, 2, 1, 2, 1, 4, 1, 4, 1, 1, 1, 2, 1, 1, 2, 32, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 2, 2, 1, 1, 1, 8, 8, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 16, 1, 2, 2, 4, 1, 1, 1, 4, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Apart from signs, this sequence is identical to A162512.

LINKS

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

G. P. Michon, Multiplicative functions

FORMULA

Multiplicative with a(p^e) = 2^(e-1) for any prime p and any positive exponent e.

a(n) = n/2 when n is a power of 2 (A000079).

a(n) = 1 when n is a squarefree number (A005117).

a(n) = 2^A046660(n) = A061142(n)/A034444(n). - R. J. Mathar, Nov 02 2016

MAPLE

A162510 := proc(n)

    local a, f;

    a := 1;

    for f in ifactors(n)[2] do

        a := a*2^(op(2, f)-1) ;

    end do:

    return a;

end proc: # R. J. Mathar, May 20 2017

MATHEMATICA

a[n_] := 2^(PrimeOmega[n] - PrimeNu[n]); Array[a, 100] (* Jean-Fran├žois Alcover, Apr 24 2017, after R. J. Mathar *)

PROG

(PARI) a(n)=my(f=factor(n)[, 2]); 2^(vecsum(f)-#f) \\ Charles R Greathouse IV, Nov 02 2016

(Python)

from sympy import factorint

from operator import mul

def a(n):

    f=factorint(n)

    return 1 if n==1 else reduce(mul, [2**(f[i] - 1) for i in f]) # Indranil Ghosh, May 20 2017

CROSSREFS

Cf. A076479, A162511, A162512.

Sequence in context: A173398 A104404 A162512 * A235388 A252733 A181876

Adjacent sequences:  A162507 A162508 A162509 * A162511 A162512 A162513

KEYWORD

easy,mult,nonn

AUTHOR

Gerard P. Michon, Jul 05 2009

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 July 25 12:29 EDT 2017. Contains 289795 sequences.