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Search: id:A010055
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| A010055 |
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1 if n is a prime power p^k (k >= 0), otherwise 0. |
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+0
10
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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Characteristic function of unit or prime powers p^k (k >= 1). Characteristic function of prime powers p^k (k >= 0). [From Daniel Forgues (squid(AT)zensearch.com), Mar 03 2009]
See A065515 for partial sums. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 22 2009]
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LINKS
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Index entries for characteristic functions
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FORMULA
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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 (reinhard.zumkeller(AT)gmail.com), May 13 2006
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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. A069513 (1 if n is a prime power p^k (k >= 1), else 0.)
Sequence in context: A131522 A144473 A011750 this_sequence A076699 A142720 A091862
Adjacent sequences: A010052 A010053 A010054 this_sequence A010056 A010057 A010058
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Charles R Greathouse IV, Mar 12 2008
Edited by Daniel Forgues (squid(AT)zensearch.com), Mar 02 2009
Comment re Galois fields moved to A069513 by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 02 2009
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