Search: id:A010055
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%I A010055
%S A010055 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,
%T A010055 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,
%U A010055 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
%N A010055 1 if n is a prime power p^k (k >= 0), otherwise 0.
%C A010055 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]
%C A010055 See A065515 for partial sums. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Nov 22 2009]
%H A010055 <a href="Sindx_Ch.html#char_fns">Index entries for characteristic functions</
               a>
%F A010055 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.
%F A010055 a(n) = 0^(A119288(n)-1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 13 2006
%o A010055 (PARI) for(n=1,120,print1(omega(n)<=1,","))
%Y A010055 Cf. A069513 (1 if n is a prime power p^k (k >= 1), else 0.)
%Y A010055 Sequence in context: A131522 A144473 A011750 this_sequence A076699 A142720 
               A091862
%Y A010055 Adjacent sequences: A010052 A010053 A010054 this_sequence A010056 A010057 
               A010058
%K A010055 nonn,new
%O A010055 1,1
%A A010055 N. J. A. Sloane (njas(AT)research.att.com).
%E A010055 More terms from Charles R Greathouse IV, Mar 12 2008
%E A010055 Edited by Daniel Forgues (squid(AT)zensearch.com), Mar 02 2009
%E A010055 Comment re Galois fields moved to A069513 by Franklin T. Adams-Watters 
               (FrankTAW(AT)Netscape.net), Nov 02 2009

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