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Number of Abelian groups of order 2n+1.
4

%I #10 Sep 23 2023 03:41:17

%S 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,

%T 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,

%U 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

%N Number of Abelian groups of order 2n+1.

%F From _Amiram Eldar_, Sep 23 2023: (Start)

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

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

%t a[n_] := FiniteAbelianGroupCount[2*n + 1]; Array[a, 100, 0] (* _Amiram Eldar_, Sep 23 2023 *)

%Y Bisection of A000688.

%Y Cf. A021002, A048651.

%K nonn,easy

%O 0,5

%A _N. J. A. Sloane_, Jan 28 2005

%E More terms from _Joshua Zucker_, May 10 2006