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