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A010055 1 if n is a prime power p^k (k >= 0), otherwise 0. 47
1, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Characteristic function of unit or prime powers p^k (k >= 1). Characteristic function of prime powers p^k (k >= 0). - Daniel Forgues, Mar 03 2009

See A065515 for partial sums. - Reinhard Zumkeller, Nov 22 2009

a(A000961(n)) = 1; a(A024619(n)) = 0. - Reinhard Zumkeller, Nov 17 2011

If n>=2, a(n)=A069513(n). - Jeppe Stig Nielsen, Feb 02 2016

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for characteristic functions

FORMULA

Dirichlet generating function: 1+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) = 0^(A119288(n)-1). - Reinhard Zumkeller, May 13 2006

a(n) = if A001221(n) <= 1 then 1 else 0. - Reinhard Zumkeller, Nov 28 2015

MAPLE

A010055 := proc(n)

    if n =1 then

        1;

    else

        if nops(ifactors(n)[2]) = 1 then

            1;

        else

            0 ;

        end if;

    end if;

end proc: # R. J. Mathar, May 25 2017

MATHEMATICA

A010055[n_]:=Boole[PrimeNu[n]<=1]; A010055/@Range[20] (* Enrique Pérez Herrero, May 30 2011 *)

{1}~Join~Table[Boole@ PrimePowerQ@ n, {n, 2, 105}] (* Michael De Vlieger, Feb 02 2016 *)

PROG

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

(Haskell)

a010055 n = if a001221 n <= 1 then 1 else 0

-- Reinhard Zumkeller, Nov 28 2015, Mar 19 2013, Nov 17 2011

CROSSREFS

Cf. A069513 (1 if n is a prime power p^k (k >= 1), else 0.)

Cf. A268340.

Cf. A100995.

Cf. A001221, A000961, A024619, A065515,

Sequence in context: A131522 A144473 A011750 * A076699 A142720 A091862

Adjacent sequences:  A010052 A010053 A010054 * A010056 A010057 A010058

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Charles R Greathouse IV, Mar 12 2008

Edited by Daniel Forgues, Mar 02 2009

Comment re Galois fields moved to A069513 by Franklin T. Adams-Watters, Nov 02 2009

STATUS

approved

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Last modified October 17 14:56 EDT 2018. Contains 316282 sequences. (Running on oeis4.)