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A320656 Number of factorizations of n into squarefree semiprimes. Number of multiset partitions of the multiset of prime factors of n, into strict pairs. 60
1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

LINKS

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

EXAMPLE

The a(4620) = 6 factorizations into squarefree semiprimes:

  4620 = (6*10*77)

  4620 = (6*14*55)

  4620 = (6*22*35)

  4620 = (10*14*33)

  4620 = (10*21*22)

  4620 = (14*15*22)

The a(4620) = 6 multiset partitions into strict pairs:

  {{1,2},{1,3},{4,5}}

  {{1,2},{1,4},{3,5}}

  {{1,2},{1,5},{3,4}}

  {{1,3},{1,4},{2,5}}

  {{1,3},{2,4},{1,5}}

  {{1,4},{2,3},{1,5}}

The a(69300) = 10 factorizations into squarefree semiprimes:

  69300 = (6*6*35*55)

  69300 = (6*10*15*77)

  69300 = (6*10*21*55)

  69300 = (6*10*33*35)

  69300 = (6*14*15*55)

  69300 = (6*15*22*35)

  69300 = (10*10*21*33)

  69300 = (10*14*15*33)

  69300 = (10*15*21*22)

  69300 = (14*15*15*22)

The a(69300) = 10 multiset partitions into strict pairs:

  {{1,2},{1,2},{3,4},{3,5}}

  {{1,2},{1,3},{2,3},{4,5}}

  {{1,2},{1,3},{2,4},{3,5}}

  {{1,2},{1,3},{2,5},{3,4}}

  {{1,2},{1,4},{2,3},{3,5}}

  {{1,2},{2,3},{1,5},{3,4}}

  {{1,3},{1,3},{2,4},{2,5}}

  {{1,3},{1,4},{2,3},{2,5}}

  {{1,3},{2,3},{2,4},{1,5}}

  {{1,4},{2,3},{2,3},{1,5}}

MATHEMATICA

bepfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[bepfacs[n/d], Min@@#>=d&]], {d, Select[Rest[Divisors[n]], SquareFreeQ[#]&&PrimeOmega[#]==2&]}]];

Table[Length[bepfacs[n]], {n, 100}]

CROSSREFS

Cf. A001055, A006881, A079275, A007716, A007717, A045778, A318871, A318953, A320462, A320655, A320658, A320659.

Sequence in context: A014359 A079998 A339661 * A322075 A288220 A173856

Adjacent sequences:  A320653 A320654 A320655 * A320657 A320658 A320659

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 18 2018

STATUS

approved

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Last modified June 16 02:14 EDT 2021. Contains 345055 sequences. (Running on oeis4.)