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Search: id:A076792
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| A076792 |
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Sum_{d divides n} d^2*(-1)^bigomega(d), where bigomega(n) = A001222(n). |
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+0
2
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| 1, -3, -8, 13, -24, 24, -48, -51, 73, 72, -120, -104, -168, 144, 192, 205, -288, -219, -360, -312, 384, 360, -528, 408, 601, 504, -656, -624, -840, -576, -960, -819, 960, 864, 1152, 949, -1368, 1080, 1344, 1224, -1680, -1152, -1848, -1560, -1752, 1584, -2208, -1640, 2353, -1803
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Multiplicative with a(p^e) = (1+(-1)^e*p^(2*e+2))/(1+p^2). Dirichlet g.f.: zeta(s)*zeta(2*s-4)/zeta(s-2). More generally, if b(n, k) = Sum_{d divides n} d^k*(-1)^bigomega(d) then b(n, k) is multiplicative and b(p^e, k) = (1+(-1)^e*p^(k*(e+1)))/(1+p^k). Dirichlet g.f. for b(n, k): zeta(s)*zeta(2*s-2*k)/zeta(s-k). b(n, 0) = A010052(n), b(n, 1) = A061020(n).
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CROSSREFS
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Cf. A008836.
Sequence in context: A094110 A084535 A051838 this_sequence A059028 A066809 A009848
Adjacent sequences: A076789 A076790 A076791 this_sequence A076793 A076794 A076795
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KEYWORD
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mult,sign
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Nov 16 2002
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