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 A249771 Irregular triangle read by rows: T(n,k) is the number of Abelian groups of order A025487(n) with k invariant factors (2 <= n, 1 <= k). 4
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 3, 3, 2, 1, 1, 1, 3, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 3, 4, 3, 2, 1, 1, 1, 5, 2, 2, 1, 3, 1, 3, 3, 2, 1, 1, 1, 1, 3, 5, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,11 COMMENTS The length of n-th row is A051282(n). Signatures differing only by a (trailing) list of ones give identical rows. LINKS Álvar Ibeas, Rows n=2..1075, flattened FORMULA T(n,1) = 1. If k > 1 and the prime signature is (e_1,...,e_s), T(n,k) = Sum(Product(A008284(e_i,k), i in I) * Product(A026820(e_i,k-1), i not in I)), where the sum is taken over nonempty subsets I of {1,...,s}. T(n,k) = A249770(A025487(n),k). T(n,1) + T(n,2) = A052304(n). EXAMPLE First rows: 1; 1,1; 1; 1,1,1; 1,1; 1,2,1,1; 1,1,1; 1; 1,2,2,1,1; 1,3; ... CROSSREFS Refinement of A050360. Last row elements: A249773. Cf. A249770, A052304. Sequence in context: A037831 A188169 A107039 * A030615 A336766 A147753 Adjacent sequences:  A249768 A249769 A249770 * A249772 A249773 A249774 KEYWORD nonn,tabf AUTHOR Álvar Ibeas, Nov 06 2014 STATUS approved

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Last modified April 14 03:13 EDT 2021. Contains 342941 sequences. (Running on oeis4.)