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A126690
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Multiplicative function defined for prime powers by a(p^k) = p + p^2 + p^3 + ... + p^(k-1) - 1 (k >= 1).
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2
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1, -1, -1, 1, -1, 1, -1, 5, 2, 1, -1, -1, -1, 1, 1, 13, -1, -2, -1, -1, 1, 1, -1, -5, 4, 1, 11, -1, -1, -1, -1, 29, 1, 1, 1, 2, -1, 1, 1, -5, -1, -1, -1, -1, -2, 1, -1, -13, 6, -4, 1, -1, -1, -11, 1, -5, 1, 1, -1, 1, -1, 1, -2, 61, 1, -1, -1, -1, 1, -1, -1, 10, -1, 1, -4, -1, 1, -1, -1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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COMMENTS
| If we change the definition to a(p^k) = p + p^2 + p^3 + ... + p^k - 1 (k >= 1) we get (-1)sigma(n), A046090.
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EXAMPLE
| a(5) = -1, a(9) = 3-1 = 2, a(45) = (-1)*2 = -2.
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MAPLE
| pksum := proc(L) local p, k ; p := op(1, L) ; k := op(2, L) ; (p^k-p)/(p-1)-1 ; end: A126690 := proc(n) local pe, a ; if n = 1 then RETURN(1) ; else a := 1 ; pe := ifactors(n)[2] ; for d in pe do a := a*pksum(d) ; od: RETURN(a) ; fi; end: for n from 1 to 120 do printf("%d, ", A126690(n)) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 08 2008]
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CROSSREFS
| Sequence in context: A111560 A113103 A033325 * A104714 A085119 A010128
Adjacent sequences: A126687 A126688 A126689 * A126691 A126692 A126693
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KEYWORD
| sign,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Feb 14 2008, based on a posting to the Sequence Fans Mailing List by Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp), Feb 02 2005
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EXTENSIONS
| Extended beyond a(30) by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 08 2008
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