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A160892 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 4. 1
15, 105, 195, 420, 465, 1365, 855, 1680, 1755, 3255, 1995, 5460, 2745, 5985, 6045, 6720, 4605, 12285, 5715, 13020, 11115, 13965, 8295, 21840, 11625, 19215, 15795, 23940, 13065, 42315, 14895, 26880, 25935, 32235, 26505, 49140, 21105, 40005, 35685, 52080, 25845 (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
a(n) = 15*A160889(n). - R. J. Mathar, Feb 07 2011
From Amiram Eldar, Nov 08 2022: (Start)
Sum_{k=1..n} a(k) ~ c * n^3, where c = 5 * Product_{p prime} (1 + 1/p^2 + 1/p^3) = 5 * A330595 = 8.7446649892... .
Sum_{k>=1} 1/a(k) = (zeta(2)*zeta(3)/15) * Product_{p prime} (1 - 2/p^3 + 1/p^5) = 0.09339604419... . (End)
MATHEMATICA
f[p_, e_] := (p^2 + p + 1)*p^(2*e - 2); a[1] = 15; a[n_] := 15*Times @@ f @@@ FactorInteger[n]; Array[a, 40] (* Amiram Eldar, Nov 08 2022 *)
PROG
(PARI) a(n) = {my(f = factor(n)); 15 * prod(i = 1, #f~, (f[i, 1]^2 + f[i, 1] + 1)*f[i, 1]^(2*f[i, 2] - 2)); } \\ Amiram Eldar, Nov 08 2022
CROSSREFS
Sequence in context: A300295 A102791 A335672 * A061550 A174385 A185129
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 19 2009
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)