cp's OEIS Frontend

A249773 Number of Abelian groups that attain the maximum number of invariant factors among those whose order is A025487(n).

%I A249773 #18 Mar 21 2015 05:16:04
%S A249773 1,1,1,1,1,1,1,1,1,1,3,1,1,1,2,1,1,1,2,3,1,1,5,1,1,2,2,1,1,3,1,1,2,2,
%T A249773 1,1,3,7,1,1,5,2,3,9,2,1,1,3,4,1,1,3,2,1,2,5,2,1,1,3,4,1,1,3,2,1,2,5,
%U A249773 10,2,1,7,9,1,3,4,5,1,13,1,3,2,1,2,5,6
%N A249773 Number of Abelian groups that attain the maximum number of invariant factors among those whose order is A025487(n).
%C A249773 The number of invariant factors (i.e., the minimum size of generating sets) of these groups is A051282(n).
%C A249773 If the n-th and m-th least (according to the ordering of A025487) prime signatures differ only by a (trailing) list of ones, a(n) = a(m).
%H A249773 Álvar Ibeas, <a href="/A249773/b249773.txt">Table of n, a(n) for n = 1..10000</a>
%F A249773 (p(e_1)^j - (p(e_1)-1)^j) * Product(p(e_i), i=j+1..s), if the prime signature is (e_i, i=1..s) and e_1 = ... = e_j != e_{j+1}.
%e A249773 A025487(15) = 72. An Abelian group of order 72 can have 1, 2, or 3 invariant factors. The instances of the last case are C18 x C2 x C2 and C6 x C6 x C2, hence a(15)=2.
%Y A249773 Last row elements of A249771. Cf. A025487, A051282.
%K A249773 nonn
%O A249773 1,11
%A A249773 _Álvar Ibeas_, Nov 07 2014