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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 July 22 16:34 EDT 2019. Contains 325224 sequences. (Running on oeis4.)