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

Author

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

Keywords

• nonn

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

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

Crossrefs

Cf. A062249, A007503.

Programs

Mathematica

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

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).

Extensions

Formula and more terms from Vladeta Jovovic, Jul 05 2001