A350159 Number of subgroups of the dicyclic group Dic_n.

3, 6, 8, 11, 10, 18, 12, 20, 19, 24, 16, 36, 18, 30, 32, 37, 22, 48, 24, 50, 40, 42, 28, 70, 37, 48, 48, 64, 34, 84, 36, 70, 56, 60, 56, 103, 42, 66, 64, 100, 46, 108, 48, 92, 90, 78, 52, 136, 63, 102, 80, 106, 58, 132, 80, 130, 88, 96, 64, 184, 66, 102, 116

Offset: 1

Author

Firdous Ahmad Mala, Dec 17 2021

Keywords

• nonn

Examples

			a(2) = A000005(4) + A000203(2) = 3+3 = 6.
Given the fact that Dic_2 is isomorphic to the quaternion group Q_8, the subgroups of Dic_2 are isomorphic to the subgroups of Q_8 which are {1}, {1,-1}, {1,i,-1,-i}, {1,j,-1,-j}, {1,k,-1,-k} and Q_8.
		

Links

• Hayder Baqer Shelash and A. R. Ashrafi, The Number of Subgroups of a Given Type in Certain Finite Groups, Iranian Journal of Mathematical Sciences and Informatics, Vol. 16, No. 2 (2021), pp. 73-87.
• Wikipedia, Dicyclic group

Crossrefs

Cf. A000005, A000203, A099777, A345628.

Programs

Mathematica

a[n_] := DivisorSigma[0, 2*n] + DivisorSigma[1, n]; Array[a, 50] (* Amiram Eldar, Dec 17 2021 *)

PARI

a(n) = numdiv(2*n) + sigma(n); \\ Michel Marcus, Dec 18 2021

Formula

a(n) = A000005(2n) + A000203(n) = A099777(n) + A000203(n).