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 A318950 Regular triangle where T(n,k) is the number of factorizations of n into factors > 1 with sum k. 5
 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 LINKS EXAMPLE Triangle begins:   0   0 1   0 0 1   0 0 0 2   0 0 0 0 1   0 0 0 0 1 1   0 0 0 0 0 0 1   0 0 0 0 0 2 0 1   0 0 0 0 0 1 0 0 1   0 0 0 0 0 0 1 0 0 1   0 0 0 0 0 0 0 0 0 0 1   0 0 0 0 0 0 2 1 0 0 0 1   0 0 0 0 0 0 0 0 0 0 0 0 1   0 0 0 0 0 0 0 0 1 0 0 0 0 1   0 0 0 0 0 0 0 1 0 0 0 0 0 0 1   0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 1   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1   0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1   0 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 1 Row 12 {0,0,0,0,0,0,2,1,0,0,0,1} corresponds to the factorizations:   . . . . . . (3*4)   (2*6) . . . (12)               (2*2*3) MATHEMATICA facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; Table[Length[Select[facs[n], Total[#]==k&]], {n, 20}, {k, n}] CROSSREFS Row sums are A001055. Column sums are A002865. Cf. A069016, A096276, A301987, A319000, A319005, A319057, A319916. Sequence in context: A138088 A112765 A105966 * A319000 A083915 A083892 Adjacent sequences:  A318947 A318948 A318949 * A318951 A318952 A318953 KEYWORD nonn,tabl AUTHOR Gus Wiseman, Oct 22 2018 STATUS approved

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Last modified June 16 19:43 EDT 2019. Contains 324155 sequences. (Running on oeis4.)