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A007428
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Moebius transform applied thrice to sequence 1,0,0,0,....
(Formerly M2271)
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5
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1, -3, -3, 3, -3, 9, -3, -1, 3, 9, -3, -9, -3, 9, 9, 0, -3, -9, -3, -9, 9, 9, -3, 3, 3, 9, -1, -9, -3, -27, -3, 0, 9, 9, 9, 9, -3, 9, 9, 3, -3, -27, -3, -9, -9, 9, -3, 0, 3, -9, 9, -9, -3, 3, 9, 3, 9, 9, -3, 27, -3, 9, -9, 0, 9, -27, -3, -9, 9, -27, -3, -3, -3, 9, -9, -9, 9, -27
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Dirichlet inverse of A007425. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 15 2010]
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| N. J. A. Sloane, Transforms
Enrique Pérez Herrero, Table of n, a(n) for n = 1..10000
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FORMULA
| Multiplicative with a(p^e) = (3 choose e) (-1)^e
Dirichlet g.f.: 1/zeta(s)^3
Contribution from Enrique Perez Herrero (psychegeometry(AT)gmail.com), Jul 12 2010: (Start)
a(n^3)=A008683(n)
a(s)=(-3)^A001221(s), being s an squarefree number: A005117 (End)
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MATHEMATICA
| Contribution from Enrique Perez Herrero (psychegeometry(AT)gmail.com), Jul 12 2010: (Start)
tau[1, n_Integer]:=1; SetAttributes[tau, Listable];
tau[k_Integer, n_Integer]:=Plus@@(tau[k-1, Divisors[n]])/; k > 1;
tau[k_Integer, n_Integer]:=Plus@@(tau[k+1, Divisors[n]]*MoebiusMu[n/Divisors[n]]); k<1;
A007428[n_]:=tau[ -3, n]; (End)
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CROSSREFS
| Consecutive nested Dirichlet convolution: A063524, A008683 or A007427 [From Enrique Perez Herrero (psychegeometry(AT)gmail.com), Jul 12 2010]
Sequence in context: A125002 A098528 A078229 * A184099 A074816 A203564
Adjacent sequences: A007425 A007426 A007427 * A007429 A007430 A007431
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KEYWORD
| sign,easy,nice,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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