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A007428 Moebius transform applied thrice to sequence 1,0,0,0,....
(Formerly M2271)
11
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. - 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.

From Enrique Pérez Herrero, Jul 12 2010: (Start)

a(n^3) = A008683(n).

a(s) = (-3)^A001221(s) provided s is a squarefree number (A005117). (End)

a(A046101(n)) = 0. - Enrique Pérez Herrero, Sep 07 2017

MAPLE

möbius := proc(a)  local b, i, mo: b := NULL:

mo := (m, n) -> `if`(irem(m, n) = 0, numtheory:-mobius(m/n), 0);

for i to nops(a) do b := b, add(mo(i, j)*a[j], j=1..i) od: [b] end:

(möbius@@3)([1, seq(0, i=1..77)]); # Peter Luschny, Sep 08 2017

MATHEMATICA

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]; (* Enrique Pérez Herrero, Jul 12 2010 *)

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. [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 October 23 23:22 EDT 2017. Contains 293833 sequences.