A101871 Number of Abelian groups of order 2n+1.

1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1

Offset: 0

Author

N. J. A. Sloane, Jan 28 2005

Keywords

• nonn
• easy

Crossrefs

Bisection of A000688.

Cf. A021002, A048651.

Programs

Mathematica

a[n_] := FiniteAbelianGroupCount[2*n + 1]; Array[a, 100, 0] (* Amiram Eldar, Sep 23 2023 *)

Formula

From Amiram Eldar, Sep 23 2023: (Start)

a(n) = A000688(2*n+1) = A000688(4*n+2).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2 * A048651 * A021002 = 1.32545452721253858057... . (End)

Extensions

More terms from Joshua Zucker, May 10 2006