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A296133
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Number of twice-factorizations of n of type (Q,R,Q).
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4
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1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 5, 1, 2, 2, 3, 1, 5, 1, 3, 2, 2, 2, 7, 1, 2, 2, 5, 1, 5, 1, 3, 3, 2, 1, 7, 1, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 9, 1, 2, 3, 6, 2, 5, 1, 3, 2, 5, 1, 9, 1, 2, 3, 3, 2, 5, 1, 7, 2, 2, 1, 9, 2, 2, 2
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OFFSET
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1,6
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LINKS
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EXAMPLE
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The a(36) = 7 twice-factorizations are (2*3)*(6), (6)*(2*3), (2*3*6), (2*18), (3*12), (4*9), (36).
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MATHEMATICA
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sfs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[sfs[n/d], Min@@#>d&]], {d, Rest[Divisors[n]]}]];
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Length[Join@@Function[fac, Select[Join@@Permutations/@sps[fac], SameQ@@Times@@@#&]]/@sfs[n]], {n, 100}]
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CROSSREFS
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Cf. A000005, A001055, A005117, A045778, A052409, A052410, A089723, A279790, A279791, A284639, A292886, A296132.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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