OFFSET
1,2
COMMENTS
From a recent general formula of Stanley's for the number of subgroups in G\times Z.
REFERENCES
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.64.
LINKS
Gheorghe Coserea, Table of n, a(n) for n = 1..20000
G. Chelnokov, M. Deryagina, A. Mednykh, On the Coverings of Amphicosms; Revised title: On the coverings of Euclidian manifolds B_1 and B_2, arXiv preprint arXiv:1502.01528 [math.AT], 2015.
V. A. Liskovets and A. Mednykh, Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces, Commun. in Algebra, 28, No. 4 (2000), 1717-1738.
FORMULA
Sum k*b(k), k|n, where b(k) is the number of n-list coverings of the Klein bottle (A046524).
MATHEMATICA
b[k_] := If[OddQ[k], DivisorSigma[0, k], (3 DivisorSigma[0, k] + DivisorSigma[1, k/2] - DivisorSigma[0, k/2])/2]; a[n_] := Sum[k*b[k], {k, Divisors[n]}]; Table[a[n], {n, 1, 56}] (* Jean-François Alcover, Jul 19 2012 *)
PROG
(PARI)
A001001(n) = sumdiv(n, d, sigma(d) * d);
A060640(n) = sumdiv(n, d, sigma(n\d) * d);
S1(n) = if (n%2, 0, A001001(n\2));
a(n) = S1(n) + S11(n) + S21(n);
vector(56, n, a(n)) \\ Gheorghe Coserea, May 05 2016
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Valery A. Liskovets
Corrected and extended by Vladeta Jovovic, Feb 03 2003
STATUS
approved