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A161024
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a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 13.
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1
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8191, 33542145, 2176512520, 68694312960, 499938962796, 8912818769400, 18895663909200, 140685952942080, 385562663380440, 2047250052649620, 2570686683371352, 18253452839731200, 15902884603186140, 77377743708174000, 132843781194153120, 288124831625379840
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OFFSET
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1,1
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^12, where c = (8191/12) * Product_{p prime} (1 + (p^11-1)/((p-1)*p^12)) = 1326.4495346... .
Sum_{k>=1} 1/a(k) = (zeta(11)*zeta(12)/8191) * Product_{p prime} (1 - 2/p^12 + 1/p^23) = 0.0001221155049... . (End)
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MATHEMATICA
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f[p_, e_] := p^(11*e - 11) * (p^12-1) / (p-1); a[1] = 8191; a[n_] := 8191 * Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* Amiram Eldar, Nov 08 2022 *)
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PROG
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(PARI) a(n) = {my(f = factor(n)); 8191 * prod(i = 1, #f~, (f[i, 1]^12 - 1)*f[i, 1]^(11*f[i, 2] - 11)/(f[i, 1] - 1)); } \\ Amiram Eldar, Nov 08 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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