A062553 Number of Abelian subgroups of the dihedral group with 2n elements.

2, 5, 5, 9, 7, 13, 9, 16, 12, 19, 13, 24, 15, 25, 19, 29, 19, 33, 21, 36, 25, 37, 25, 44, 28, 43, 31, 48, 31, 53, 33, 54, 37, 55, 39, 63, 39, 61, 43, 68, 43, 71, 45, 72, 51, 73, 49, 82, 52, 81, 55, 84, 55, 89, 59, 92, 61, 91, 61, 102, 63, 97, 69, 103, 69, 107, 69, 108, 73

Offset

1,1

Comments

The rank of the fundamental group with genus one of the D_2n; cobordism category in dimension 1+1, with D_2n the dihedral group of order 2n. - _C. Segovia_, Dec 05 2012

Links

Table of n, a(n) for n=1..69.

C. Segovia, The classifying space of the 1+1 dimensional G-cobordism category, arXiv:1211.2144 [math.AT], 2012-2013.

Formula

a(n) = n + tau(n) if n is odd, (3/2)*n + tau(n) if n is even, where tau(n) = the number of divisors of n (A000005).

Mathematica

a[n_] := If[OddQ[n], n, 3n/2] + DivisorSigma[0, n];
Array[a, 69] (* Jean-François Alcover, Feb 24 2019 *)

Crossrefs

Cf. A062249, A007503.

Sequence in context: A284169 A152781 A200242 * A126357 A377809 A070243

Adjacent sequences: A062550 A062551 A062552 * A062554 A062555 A062556

Keyword

nonn

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 02 2001

Extensions

Formula and more terms from Vladeta Jovovic, Jul 05 2001

Status

approved