A101876 Number of Abelian groups of order 4n.

2, 3, 2, 5, 2, 3, 2, 7, 4, 3, 2, 5, 2, 3, 2, 11, 2, 6, 2, 5, 2, 3, 2, 7, 4, 3, 6, 5, 2, 3, 2, 15, 2, 3, 2, 10, 2, 3, 2, 7, 2, 3, 2, 5, 4, 3, 2, 11, 4, 6, 2, 5, 2, 9, 2, 7, 2, 3, 2, 5, 2, 3, 4, 22, 2, 3, 2, 5, 2, 3, 2, 14, 2, 3, 4, 5, 2, 3, 2, 11, 10, 3, 2, 5, 2, 3, 2, 7, 2, 6, 2, 5, 2, 3, 2, 15, 2, 6, 4, 10, 2

Offset: 1

Author

N. J. A. Sloane, Jan 28 2005

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Bisection of A101872, quadrisection of A000688.

Cf. A000041, A021002, A048651.

Programs

Mathematica

a[n_] := FiniteAbelianGroupCount[4*n]; Array[a, 100] (* Amiram Eldar, Sep 23 2023*)

PARI

A101876(n) = factorback(apply(e -> numbpart(e),factor(4*n)[,2])); \\ Antti Karttunen, Sep 27 2018

Formula

a(n) = A000688(4*n). - Antti Karttunen, Sep 27 2018

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (4 - 6 * A048651) * A021002 = 5.20306278505563943501... . - Amiram Eldar, Sep 23 2023

Extensions

More terms from Joshua Zucker, May 10 2006