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A160890
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a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 3.
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1
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7, 21, 28, 42, 42, 84, 56, 84, 84, 126, 84, 168, 98, 168, 168, 168, 126, 252, 140, 252, 224, 252, 168, 336, 210, 294, 252, 336, 210, 504, 224, 336, 336, 378, 336, 504, 266, 420, 392, 504, 294, 672, 308, 504, 504, 504, 336, 672, 392, 630, 504, 588, 378, 756
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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^2 + O(n*log(n)), where c = 105/(2*Pi^2) = 5.319362... . (End)
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MATHEMATICA
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With[{b = 3}, Table[((2^b - 1)/EulerPhi[n]) DivisorSum[n, MoebiusMu[n/#] #^(b - 1) &], {n, 54}]] (* Michael De Vlieger, Nov 23 2017 *)
f[p_, e_] := (p + 1)*p^(e - 1); a[1] = 7; a[n_] := 7*Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Nov 08 2022 *)
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PROG
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(PARI) a(n) = {my(f = factor(n)); 7 * prod(i = 1, #f~, (f[i, 1] + 1)*f[i, 1]^(f[i, 2] - 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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