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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

%I

%S 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,

%T 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,

%U 1,0,0,0,0,1,0,0,1,0,0,0,0,1,0,1,1,1,1

%N Number of factorizations of n into squarefree semiprimes. Number of multiset partitions of the multiset of prime factors of n, into strict pairs.

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

%e 4620 = (6*10*77)

%e 4620 = (6*14*55)

%e 4620 = (6*22*35)

%e 4620 = (10*14*33)

%e 4620 = (10*21*22)

%e 4620 = (14*15*22)

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

%e {{1,2},{1,3},{4,5}}

%e {{1,2},{1,4},{3,5}}

%e {{1,2},{1,5},{3,4}}

%e {{1,3},{1,4},{2,5}}

%e {{1,3},{2,4},{1,5}}

%e {{1,4},{2,3},{1,5}}

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

%e 69300 = (6*6*35*55)

%e 69300 = (6*10*15*77)

%e 69300 = (6*10*21*55)

%e 69300 = (6*10*33*35)

%e 69300 = (6*14*15*55)

%e 69300 = (6*15*22*35)

%e 69300 = (10*10*21*33)

%e 69300 = (10*14*15*33)

%e 69300 = (10*15*21*22)

%e 69300 = (14*15*15*22)

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

%e {{1,2},{1,2},{3,4},{3,5}}

%e {{1,2},{1,3},{2,3},{4,5}}

%e {{1,2},{1,3},{2,4},{3,5}}

%e {{1,2},{1,3},{2,5},{3,4}}

%e {{1,2},{1,4},{2,3},{3,5}}

%e {{1,2},{2,3},{1,5},{3,4}}

%e {{1,3},{1,3},{2,4},{2,5}}

%e {{1,3},{1,4},{2,3},{2,5}}

%e {{1,3},{2,3},{2,4},{1,5}}

%e {{1,4},{2,3},{2,3},{1,5}}

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

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

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

%K nonn

%O 1

%A _Gus Wiseman_, Oct 18 2018

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Last modified July 28 17:15 EDT 2021. Contains 346335 sequences. (Running on oeis4.)