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Search: id:A046970
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| A046970 |
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Generated from Riemann Zeta function: coefficients in series expansion of Zeta(n+2)/Zeta(n). |
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+0
4
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| 1, -3, -8, -3, -24, 24, -48, -3, -8, 72, -120, 24, -168, 144, 192, -3, -288, 24, -360, 72, 384, 360, -528, 24, -24, 504, -8, 144, -840, -576, -960, -3, 960, 864, 1152, 24, -1368, 1080, 1344, 72, -1680, -1152, -1848, 360, 192, 1584, -2208, 24, -48, 72, 2304, 504, -2808, 24, 2880, 144, 2880, 2520, -3480, -576
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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B(n+2) = -B(n)*((n+2)*(n+1)/(4pi^2))*z(n+2)/z(n) = -B(n)*((n+2)*(n+1)/(4pi^2))*Sum(j=1, infinity) [ a(j)/j^(n+2) ]
Apart from signs also Sum_{d|n} core(d)^2*mu(n/d) where core(x) is the squarefree part of x. - Benoit Cloitre (benoit7848c(AT)orange.fr), May 31 2002
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REFERENCES
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M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, 1965, pp. 805-811.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
Wikipedia, Riemann zeta function.
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FORMULA
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Multiplicative with a(p^e) = 1-p^2. a(n) = Sum_{d|n} mu(d)*d^2.
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EXAMPLE
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a(3) = -8 because the divisors of 3 are {1, 3}, and mu(1)*1^2 + mu(3)*3^2 = -8.
a(4) = -3 because the divisors of 4 are {1, 2, 4}, and mu(1)*1^2 + mu(2)*2^2 + mu(4)*4^2 = -3
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MATHEMATICA
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muDD[d_] := MoebiusMu[d]*d^2; Table[Plus @@ muDD[Divisors[n]], {n, 60}] (Lopez)
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PROGRAM
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(PARI) A046970(n)=sumdiv(n, d, d^2*moebius(d)) (Benoit Cloitre)
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CROSSREFS
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Cf. A027641 and A027642.
Adjacent sequences: A046967 A046968 A046969 this_sequence A046971 A046972 A046973
Sequence in context: A016623 A046543 A035292 this_sequence A058936 A002017 A086179
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KEYWORD
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sign,mult
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AUTHOR
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Douglas Stoll, dougstoll(AT)email.msn.com
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EXTENSIONS
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Corrected and extended by Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 25 2001
Additional comments from Wilfredo Lopez (chakotay147138274(AT)yahoo.com), Jul 01 2005
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