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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

Table of n, a(n) for n=1..87.

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.)