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A063453
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Multiplicative with a(p^e) = 1-p^3.
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8
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1, -7, -26, -7, -124, 182, -342, -7, -26, 868, -1330, 182, -2196, 2394, 3224, -7, -4912, 182, -6858, 868, 8892, 9310, -12166, 182, -124, 15372, -26, 2394, -24388, -22568, -29790, -7, 34580, 34384, 42408, 182, -50652, 48006, 57096, 868, -68920, -62244, -79506, 9310, 3224, 85162, -103822, 182
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| More generally, Dirichlet g.f. for Sum_{d|n} mu(d)*d^k, the Dirichlet inverse of the Jordan function J_k, is zeta(s)/zeta(s-k).
Apart from different signs also Sum_{d|n} core(d)^3*mu(n/d) where core(x) is the squarefree part of x. - Benoit Cloitre, May 31 2002
Dirichlet inverse of A059376. [From R. J. Mathar, Jul 15 2010]
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REFERENCES
| T. M. Apostol, Introduction to Analytic Number Theory, Springer, 1986.
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
P. G. Brown, Some comments on inverse arithmetic functions, Math. Gaz. 89 (516) (2005) 403-408.
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FORMULA
| a(n) = Sum_{d|n} mu(d)*d^3.
Dirichlet g.f.: zeta(s)/zeta(s-3).
A023900(n) | a(n). - R. J. Mathar, Mar 30 2011
a(n)= product_{p|n}(1-p^3), n>=2, p prime, a(1)=1. a(n)= J_{-3}(n)*n^3, with the Jordan function J_k(n). See the Apostol reference, p. 48, exercise 17. - Wolfdieter Lang, Jun 16 2011.
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MAPLE
| Jinvk := proc(n, k) local a, f, p ; a := 1 ; for f in ifactors(n)[2] do p := op(1, f) ; a := a*(1-p^k) ; end do: a ; end proc:
A063453 := proc(n) Jinvk(n, 3) ; end proc: # R. J. Mathar, Jul 04 2011
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MATHEMATICA
| a[n_] := Total[MoebiusMu[#]*#^3& /@ Divisors[n]]; Table[a[n], {n, 1, 48}] (* From Jean-François Alcover, Jul 26 2011 *)
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PROG
| (Haskell)
a063453 = product . map ((1 -) . (^ 3)) . a027748_row
-- Reinhard Zumkeller, Jan 19 2012
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CROSSREFS
| Cf. A023900, A046970.
Cf. A027748.
Sequence in context: A081298 A012490 A157702 * A098127 A131905 A110927
Adjacent sequences: A063450 A063451 A063452 * A063454 A063455 A063456
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KEYWORD
| mult,sign
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 26 2001
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