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A160913
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a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 8.
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1
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255, 32385, 278715, 2072640, 4980405, 35396805, 35000535, 132648960, 203183235, 632511435, 496922835, 2265395520, 1333405965, 4445067945, 5443582665, 8489533440, 6539772585, 25804270845, 12663182955, 40480731840, 38255584755, 63109200045, 39465022215, 144985313280
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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^7, where c = (255/7) * Product_{p prime} (1 + (p^6-1)/((p-1)*p^7)) = 70.419647503... .
Sum_{k>=1} 1/a(k) = (zeta(6)*zeta(7)/255) * Product_{p prime} (1 - 2/p^7 + 1/p^13) = 0.003956793297... . (End)
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MATHEMATICA
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f[p_, e_] := p^(6*e - 6) * (p^7-1) / (p-1); a[1] = 255; a[n_] := 255 * 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)); 255 * prod(i = 1, #f~, (f[i, 1]^7 - 1)*f[i, 1]^(6*f[i, 2] - 6)/(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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