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A007432 Moebius transform applied thrice to natural numbers.
(Formerly M0031)
2
1, -1, 0, 1, 2, 0, 4, 1, 3, -2, 8, 0, 10, -4, 0, 2, 14, -3, 16, 2, 0, -8, 20, 0, 13, -10, 8, 4, 26, 0, 28, 4, 0, -14, 8, 3, 34, -16, 0, 2, 38, 0, 40, 8, 6, -20, 44, 0, 31, -13, 0, 10, 50, -8, 16, 4, 0, -26, 56, 0, 58, -28, 12, 8, 20, 0, 64, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

REFERENCES

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

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210.

N. J. A. Sloane, Transforms

FORMULA

Multiplicative with a(p^e) = sum (-1)^k (3 choose k)p^(e-k)[e>=k], k=0..3

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

a(n)=Sum{d|n} tau_{-3}(d)*n/d = Sum{d|n} tau_{-2}(d)*phi(n/d), where tau_{-3} is A007428 and tau_{-2} A007427. - Enrique Pérez Herrero, Jan 19 2013

MATHEMATICA

a[p_, e_] := Sum[ (-1)^k*Binomial[3, k]*p^(e - k), {k, 0, Min[e, 3]}]; a[n_] := Times @@ Apply[a, FactorInteger[n], {1}]; a[1] = 1; Table[ a[n], {n, 1, 68}] (* Jean-François Alcover, Dec 28 2011, after formula *)

CROSSREFS

Cf. A007431

Sequence in context: A154794 A177264 A020781 * A079124 A242071 A176910

Adjacent sequences:  A007429 A007430 A007431 * A007433 A007434 A007435

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.