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A321817
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a(n) = Sum_{d|n, n/d odd} d^6 for n > 0.
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3
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1, 64, 730, 4096, 15626, 46720, 117650, 262144, 532171, 1000064, 1771562, 2990080, 4826810, 7529600, 11406980, 16777216, 24137570, 34058944, 47045882, 64004096, 85884500, 113379968, 148035890, 191365120, 244156251, 308915840, 387952660
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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^(6*e) and a(p^e) = (p^(6*e+6)-1)/(p^6-1) for p > 2.
Sum_{k=1..n} a(k) ~ c * n^7, where c = 127*zeta(7)/896 = 0.142924... . (End)
Dirichlet g.f.: zeta(s)*zeta(s-6)*(1-1/2^s). - Amiram Eldar, Jan 08 2023
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MATHEMATICA
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a[n_] := DivisorSum[n, #^6 &, OddQ[n/#] &]; Array[a, 30] (* Amiram Eldar, Nov 02 2022 *)
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PROG
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(PARI) apply( A321817(n)=sumdiv(n, d, if(bittest(n\d, 0), d^6)), [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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