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A069513 Characteristic function of the prime powers p^k, k >= 1. 15
0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also, number of Galois fields of order n. - Charles R Greathouse IV, Mar 12 2008

If n >= 2, a(n) = A010055(n).

LINKS

Daniel Forgues, Table of n, a(n) for n=1..100000.

FORMULA

a(n) = Sum_{d divides n} bigomega(d)*mu(n/d); equivalently, Sum_{d divides n} a(d) = bigomega(n); equivalently, Möbius transform of bigomega(n).

Dirichlet g.f.: ppzeta(s). Here ppzeta(s) = Sum_{p prime} Sum_{k>=1} 1/(p^k)^s. Note that ppzeta(s) = Sum_{p prime} 1/(p^s - 1) = Sum_{k>=1} primezeta(k*s). - Franklin T. Adams-Watters, Sep 11 2005

a(n) = floor(1/A001221(n)), for n > 1. - Enrique Pérez Herrero, Jun 01 2011

MAPLE

A069513 := proc(n)

    if n = 1 then

        0 ;

    elif A001221(n) > 1 then

        0;

    else

        1 ;

    end if ;

end proc:

seq(A069513(n), n=1..80) ; # R. J. Mathar, Nov 02 2016

MATHEMATICA

A069513[n_]:=Boole[PrimeNu[n]==1]; A069513/@Range[20] (* Enrique Pérez Herrero, May 30 2011 *)

PROG

(PARI) for(n=1, 120, print1(omega(n)==1, ", "))

(Haskell)

a069513 1 = 0

a069513 n = a010055 n  -- Reinhard Zumkeller, Mar 19 2013

CROSSREFS

Cf. A246655, A010055, A001222, A008683.

The partial sums of this sequence give A025528. - Daniel Forgues, Mar 02 2009

Cf. A014963, A003418. - Enrique Pérez Herrero, Jun 01 2011

Sequence in context: A053867 A189727 A268411 * A092248 A106743 A284944

Adjacent sequences:  A069510 A069511 A069512 * A069514 A069515 A069516

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Apr 15 2002

EXTENSIONS

Moved original definition to formula line. Used comment (that I previously added) as definition. - Daniel Forgues, Mar 08 2009

Edited by Franklin T. Adams-Watters, Nov 02 2009

STATUS

approved

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Last modified May 22 18:53 EDT 2019. Contains 323481 sequences. (Running on oeis4.)