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A321553
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a(n) = Sum_{d|n} (-1)^(n/d+1)*d^8.
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7
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1, 255, 6562, 65279, 390626, 1673310, 5764802, 16711423, 43053283, 99609630, 214358882, 428360798, 815730722, 1470024510, 2563287812, 4278124287, 6975757442, 10978587165, 16983563042, 25499674654, 37828630724, 54661514910, 78310985282, 109660357726, 152588281251, 208011334110, 282472589764
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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) = (127*2^(8*e+1)+1)/255, and a(p^e) = (p^(8*e+8) - 1)/(p^8 - 1) if p > 2.
Sum_{k=1..n} a(k) ~ c * n^9, where c = 85*zeta(9)/768 = 0.110899... . (End)
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MATHEMATICA
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Table[Total[(-1)^(n/#+1) #^8&/@Divisors[n]], {n, 30}] (* Harvey P. Dale, May 05 2021 *)
f[p_, e_] := (p^(8*e + 8) - 1)/(p^8 - 1); f[2, e_] := (127*2^(8*e + 1) + 1)/255; 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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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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