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Search: id:A069513
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| A069513 |
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Characteristic function of the prime powers p^k, k >= 1. |
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+0
2
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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; listen)
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OFFSET
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1,1
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COMMENT
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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
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Daniel Forgues, Table of n, a(n) for n=1,...,100000.
Charles R Greathouse IV, Home Page [in lieu of email address]
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FORMULA
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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.
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PROGRAM
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(PARI) for(n=1, 120, print1(omega(n)==1, ", "))
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CROSSREFS
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Cf. A010055, A001222, A008683.
The partial sums of this sequence give A025528. [From Daniel Forgues (squid(AT)zensearch.com), Mar 02 2009]
Sequence in context: A131719 A100656 A053867 this_sequence A092248 A106743 A011558
Adjacent sequences: A069510 A069511 A069512 this_sequence A069514 A069515 A069516
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KEYWORD
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easy,nonn,new
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 15 2002
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EXTENSIONS
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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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