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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. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

Vaclav Kotesovec, Plot of Sum_{k=1..n} a(k) / (108*n^2/Pi^6) for n = 1..1000000

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

Sum_{k=1..n} a(k) ~ 108 * n^2 / Pi^6. - Vaclav Kotesovec, Nov 04 2018

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: A305796 A020781 A327883 * 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 July 2 11:54 EDT 2020. Contains 335398 sequences. (Running on oeis4.)