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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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1
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| 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
| Cf. A008836.
Sequence in context: A194427 A185954 A051838 * A146939 A181540 A059028
Adjacent sequences: A076789 A076790 A076791 * A076793 A076794 A076795
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KEYWORD
| mult,sign
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 16 2002
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