OFFSET
1,1
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 19 2009
STATUS
approved