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A321557
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a(n) = Sum_{d|n} (-1)^(n/d+1)*d^12.
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8
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1, 4095, 531442, 16773119, 244140626, 2176254990, 13841287202, 68702695423, 282430067923, 999755863470, 3138428376722, 8913939907598, 23298085122482, 56680071092190, 129746582562692, 281406240452607, 582622237229762, 1156551128144685, 2213314919066162, 4094999772632494
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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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Multiplicative with a(2^e) = (2047*2^(12*e+12)+1)/4095, and a(p^e) = (p^(12*e+12) - 1)/(p^12 - 1) if p > 2.
Sum_{k=1..n} a(k) ~ c * n^13, where c = 315*zeta(13)/4096 = 0.0769137... . (End)
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MATHEMATICA
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f[p_, e_] := (p^(12*e + 12) - 1)/(p^12 - 1); f[2, e_] := (2047*2^(12*e + 1) + 1)/4095; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Nov 11 2022 *)
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PROG
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(PARI) apply( A321557(n)=sumdiv(n, d, (-1)^(n\d-1)*d^12), [1..30]) \\ M. F. Hasler, Nov 26 2018
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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