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A321820
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a(n) = Sum_{d|n, n/d odd} d^12 for n > 0.
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3
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1, 4096, 531442, 16777216, 244140626, 2176786432, 13841287202, 68719476736, 282430067923, 1000000004096, 3138428376722, 8916117225472, 23298085122482, 56693912379392, 129746582562692, 281474976710656, 582622237229762, 1156833558212608
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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) = 2^(12*e) and a(p^e) = (p^(12*e+12)-1)/(p^12-1) for p > 2.
Sum_{k=1..n} a(k) ~ c * n^13, where c = 8191*zeta(13)/106496 = 0.0769231... . (End)
Dirichlet g.f.: zeta(s)*zeta(s-12)*(1-1/2^s). - Amiram Eldar, Jan 09 2023
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MATHEMATICA
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a[n_] := DivisorSum[n, #^12 &, OddQ[n/#] &]; Array[a, 20] (* Amiram Eldar, Nov 02 2022 *)
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PROG
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(PARI) apply( A321820(n)=sumdiv(n, d, if(bittest(n\d, 0), 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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