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A069513
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Characteristic function of the prime powers p^k, k >= 1.
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4
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| Also, number of Galois fields of order n. - Charles R Greathouse IV, Mar 12 2008
If n>=2, a(n)=A010055(n).
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LINKS
| Daniel Forgues, Table of n, a(n) for n=1,...,100000.
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FORMULA
| a(n) = Sum(d divides n,bigomega(d)*mu(n/d)); equivalently, Sum(d divides n,a(d)) = bigomega(n); equivalently, Moebius transform of bigomega(n).
Dirichlet generating function: 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
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MATHEMATICA
| A069513[n_]:=Boole[PrimeNu[n]==1]; A069513/@Range[20] (* Enrique Perez Herrero, May 30 2011 *)
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PROG
| (PARI) for(n=1, 120, print1(omega(n)==1, ", "))
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CROSSREFS
| Cf. A010055, A001222, A008683.
The partial sums of this sequence give A025528. [From Daniel Forgues (squid(AT)zensearch.com), Mar 02 2009]
Cf. A014963, A003418. [From Enrique Pérez Herrero (psychgeometry(AT)gmail.com), Jun 01 2011]
Sequence in context: A131719 A100656 A053867 * A092248 A106743 A011558
Adjacent sequences: A069510 A069511 A069512 * A069514 A069515 A069516
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KEYWORD
| easy,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 15 2002
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EXTENSIONS
| Moved original definition to formula line. Used comment (that I previously added) as definition. - Daniel Forgues (squid(AT)zensearch.com), Mar 08 2009
Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 02 2009
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