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A321549
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a(n) = Sum_{d|n} (-1)^(d-1)*d^10.
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2
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1, -1023, 59050, -1049599, 9765626, -60408150, 282475250, -1074791423, 3486843451, -9990235398, 25937424602, -61978820950, 137858491850, -288972180750, 576660215300, -1100586419199, 2015993900450, -3567040850373, 6131066257802, -10249991283974, 16680163512500, -26533985367846, 41426511213650
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} (-1)^(k-1)*k^10*x^k/(1 - x^k). - Ilya Gutkovskiy, Dec 23 2018
Multiplicative with a(2^e) = 2 - (2^(10*e + 10) - 1)/1023, and a(p^e) = (p^(10*e + 10) - 1)/(p^10 - 1) for p > 2. - Amiram Eldar, Nov 04 2022
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MATHEMATICA
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f[p_, e_] := (p^(10*e + 10) - 1)/(p^10 - 1); f[2, e_] := 2 - (2^(10*e + 10) - 1)/1023; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 24] (* Amiram Eldar, Nov 04 2022 *)
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PROG
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(PARI) apply( a(n)=sumdiv(n, d, (-1)^(d-1)*d^10), [1..30]) \\ M. F. Hasler, Nov 26 2018
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CROSSREFS
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KEYWORD
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sign,mult
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AUTHOR
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STATUS
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approved
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