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A161215
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a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 17.
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3
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131071, 8589737985, 2821088318560, 281468534292480, 4999961852994576, 184880022956829600, 725978907114673600, 9223160931695984640, 40479533921803813920, 327672500035999538160, 602267704294826658336, 6058148592249392332800, 7268068365187380400720
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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^16, where c = (131071/16) * Product_{p prime} (1 + (p^15-1)/((p-1)*p^16)) = 15921.65841... .
Sum_{k>=1} 1/a(k) = (zeta(15)*zeta(16)/131071) * Product_{p prime} (1 - 2/p^16 + 1/p^31) = 7.6295695155...*10^(-6). (End)
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MATHEMATICA
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f[p_, e_] := p^(15*e - 15) * (p^16-1) / (p-1); a[1] = 131071; a[n_] := 131071 * 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)); 131071 * prod(i = 1, #f~, (f[i, 1]^16 - 1)*f[i, 1]^(15*f[i, 2] - 15)/(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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