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

1,1

Links

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

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

Mathematica

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

Prog

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

Crossrefs

Bisection of A101872, quadrisection of A000688.

Cf. A000041, A021002, A048651.

Sequence in context: A056927 A094290 A265111 * A260218 A087986 A129088

Adjacent sequences: A101873 A101874 A101875 * A101877 A101878 A101879

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 28 2005

Extensions

More terms from Joshua Zucker, May 10 2006

Status

approved