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A007428 Moebius transform applied thrice to sequence 1,0,0,0,....
(Formerly M2271)
10
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; text; internal format)
OFFSET

1,2

COMMENTS

Dirichlet inverse of A007425. [From R. J. Mathar, Jul 15 2010]

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Enrique Pérez Herrero, Table of n, a(n) for n = 1..10000

N. J. A. Sloane, Transforms

FORMULA

Multiplicative with a(p^e) = (3 choose e) (-1)^e

Dirichlet g.f.: 1/zeta(s)^3

Contribution from Enrique Pérez Herrero, Jul 12 2010: (Start)

a(n^3)=A008683(n)

a(s)=(-3)^A001221(s), being s an squarefree number: A005117 (End)

MATHEMATICA

Contribution from Enrique Pérez Herrero, 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)

PROG

(Haskell)

a007428 n = product

   [a007318' 3 e * cycle [1, -1] !! fromIntegral e | e <- a124010_row n]

-- Reinhard Zumkeller, Oct 09 2013

CROSSREFS

Consecutive nested Dirichlet convolution: A063524, A008683 or A007427 [From Enrique Pérez Herrero, Jul 12 2010]

Cf. A124010.

Sequence in context: A078229 A222292 A245441 * A184099 A074816 A203564

Adjacent sequences:  A007425 A007426 A007427 * A007429 A007430 A007431

KEYWORD

sign,easy,nice,mult

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 22 22:17 EDT 2017. Contains 283901 sequences.