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A249773 Number of Abelian groups that attain the maximum number of invariant factors among those whose order is A025487(n). 3
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, 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, 10, 2, 1, 7, 9, 1, 3, 4, 5, 1, 13, 1, 3, 2, 1, 2, 5, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

COMMENTS

The number of invariant factors (i.e., the minimum size of generating sets) of these groups is A051282(n).

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).

LINKS

Álvar Ibeas, Table of n, a(n) for n = 1..10000

FORMULA

(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}.

EXAMPLE

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.

CROSSREFS

Last row elements of A249771. Cf. A025487, A051282.

Sequence in context: A322127 A282496 A253238 * A030369 A298667 A226166

Adjacent sequences:  A249770 A249771 A249772 * A249774 A249775 A249776

KEYWORD

nonn

AUTHOR

Álvar Ibeas, Nov 07 2014

STATUS

approved

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Last modified June 6 17:20 EDT 2020. Contains 334829 sequences. (Running on oeis4.)