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Search: id:A055615
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| 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, 26, 0, 0, -29, -30, -31, 0, 33, 34, 35, 0, -37, 38, 39, 0, -41, -42, -43, 0, 0, 46, -47, 0, 0, 0, 51, 0, -53, 0, 55, 0, 57, 58, -59, 0, -61, 62, 0, 0, 65, -66, -67, 0, 69, -70, -71, 0
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Dirichlet inverse of n.
Absolute values give n if n is square-free otherwise 0.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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Dirichlet g.f.: 1/zeta(s-1).
Multiplicative with a(p^e) = -p*0^(e-1), e>0 and p prime. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 17 2003
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
Dirichlet generating function for the absolute value: zeta(s-1)/zeta(2s-2). - Franklin T. Adams-Watters, Sep 11 2005.
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PROGRAM
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(PARI) a(n)=n*moebius(n)
(PARI) a(n)=if(n<1, 0, direuler(p=2, n, 1-p*X)[n])
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CROSSREFS
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Cf. A000027, A023900. Moebius transform of A023900.
Cf. A008683, A062004.
Sequence in context: A128214 A145105 A140700 this_sequence A049268 A004179 A122830
Adjacent sequences: A055612 A055613 A055614 this_sequence A055616 A055617 A055618
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KEYWORD
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sign,easy,nice,mult
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AUTHOR
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Michael Somos, Jun 04 2000
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