Search: id:A055615
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%I A055615
%S A055615 1,2,3,0,5,6,7,0,0,10,11,0,13,14,15,0,17,0,19,0,21,22,23,0,0,
%T A055615 26,0,0,29,30,31,0,33,34,35,0,37,38,39,0,41,42,43,0,0,46,47,0,
%U A055615 0,0,51,0,53,0,55,0,57,58,59,0,61,62,0,0,65,66,67,0,69,70,71,0
%V A055615 1,-2,-3,0,-5,6,-7,0,0,10,-11,0,-13,14,15,0,-17,0,-19,0,21,22,-23,0,0,
%W A055615 26,0,0,-29,-30,-31,0,33,34,35,0,-37,38,39,0,-41,-42,-43,0,0,46,-47,0,
%X A055615 0,0,51,0,-53,0,55,0,57,58,-59,0,-61,62,0,0,65,-66,-67,0,69,-70,-71,0
%N A055615 a(n)=n*moebius(n) (cf. A008683).
%C A055615 Dirichlet inverse of n.
%C A055615 Absolute values give n if n is square-free otherwise 0.
%H A055615 T. D. Noe, <a href="b055615.txt">Table of n, a(n) for n=1..1000</a>
%F A055615 Dirichlet g.f.: 1/zeta(s-1).
%F A055615 Multiplicative with a(p^e) = -p*0^(e-1), e>0 and p prime. - Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 17 2003
%F A055615 Conjectures: lim b->1+ Sum n=1..inf a(n)*b^(-n) = -12 and lim b->1- Sum 
               n=1..inf a(n)*b^n = -12 (+ indicates that b decreases to 1, - indicates 
               it increases to 1), both considering that zeta(-1) = -1/12 and calculations 
               (more generally mu(n)*n^s is Abel summable to zeta(-s)). - Gerald 
               McGarvey (Gerald.McGarvey(AT)comcast.net), Sep 26 2004
%F A055615 Dirichlet generating function for the absolute value: zeta(s-1)/zeta(2s-2). 
               - Franklin T. Adams-Watters, Sep 11 2005.
%o A055615 (PARI) a(n)=n*moebius(n)
%o A055615 (PARI) a(n)=if(n<1,0,direuler(p=2,n,1-p*X)[n])
%Y A055615 Cf. A000027, A023900. Moebius transform of A023900.
%Y A055615 Cf. A008683, A062004.
%Y A055615 Sequence in context: A128214 A145105 A140700 this_sequence A049268 A004179 
               A122830
%Y A055615 Adjacent sequences: A055612 A055613 A055614 this_sequence A055616 A055617 
               A055618
%K A055615 sign,easy,nice,mult
%O A055615 1,2
%A A055615 Michael Somos, Jun 04 2000

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