cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A101876 Number of Abelian groups of order 4n.

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%I A101876 #15 Sep 23 2023 03:48:18
%S A101876 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,
%T A101876 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,
%U A101876 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
%N A101876 Number of Abelian groups of order 4n.
%H A101876 Antti Karttunen, <a href="/A101876/b101876.txt">Table of n, a(n) for n = 1..65537</a>
%F A101876 a(n) = A000688(4*n). - _Antti Karttunen_, Sep 27 2018
%F A101876 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (4 - 6 * A048651) * A021002 = 5.20306278505563943501... . - _Amiram Eldar_, Sep 23 2023
%t A101876 a[n_] := FiniteAbelianGroupCount[4*n]; Array[a, 100] (* _Amiram Eldar_, Sep 23 2023*)
%o A101876 (PARI) A101876(n) = factorback(apply(e -> numbpart(e),factor(4*n)[,2])); \\ _Antti Karttunen_, Sep 27 2018
%Y A101876 Bisection of A101872, quadrisection of A000688.
%Y A101876 Cf. A000041, A021002, A048651.
%K A101876 nonn,easy
%O A101876 1,1
%A A101876 _N. J. A. Sloane_, Jan 28 2005
%E A101876 More terms from _Joshua Zucker_, May 10 2006