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A160956
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a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 9.
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1
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511, 130305, 1676080, 16679040, 49902216, 427400400, 490968800, 2134917120, 3665586960, 12725065080, 10953738768, 54707251200, 34736533160, 125197044000, 163679268480, 273269391360, 222788253240, 934724674800, 482144484080, 1628808330240, 1610377664000
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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^8, where c = (511/8) * Product_{p prime} (1 + (p^7-1)/((p-1)*p^8)) = 123.8157549... .
Sum_{k>=1} 1/a(k) = (zeta(7)*zeta(8)/511) * Product_{p prime} (1 - 2/p^8 + 1/p^15) = 0.001965303453... . (End)
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MATHEMATICA
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A160956[n_] := DivisorSum[n, MoebiusMu[n/#]*#^(9 - 1)/EulerPhi[n] &]; Table[511*A160956[n], {n, 1, 50}] (* G. C. Greubel, Dec 12 2017 *)
f[p_, e_] := p^(7*e - 7) * (p^8-1) / (p-1); a[1] = 511; a[n_] := 511 * 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)); 511 * prod(i = 1, #f~, (f[i, 1]^8 - 1)*f[i, 1]^(7*f[i, 2] - 7)/(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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