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A160890 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 3. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Jin Ho Kwak and Jaeun Lee, Enumeration of graph coverings, surface branched coverings and related group theory, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161. See p. 134.
FORMULA
From Amiram Eldar, Nov 08 2022: (Start)
a(n) = 7 * A001615(n).
Sum_{k=1..n} a(k) ~ c * n^2 + O(n*log(n)), where c = 105/(2*Pi^2) = 5.319362... . (End)
MATHEMATICA
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 *)
PROG
(PARI) A160890(n) = ((7/eulerphi(n))*sumdiv(n, d, moebius(n/d)*(d^2))); \\ Antti Karttunen, Nov 23 2017
(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
CROSSREFS
Sequence in context: A219036 A063469 A155131 * A319527 A297178 A325553
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 19 2009
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)