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 A327523 Number of factorizations of the n-th number with distinct prime multiplicities A130091(n) into numbers > 1 with distinct prime multiplicities. 8
 1, 1, 1, 2, 1, 1, 3, 2, 1, 3, 1, 5, 1, 3, 1, 3, 1, 5, 2, 3, 3, 1, 1, 7, 1, 5, 1, 1, 3, 3, 1, 9, 2, 3, 3, 1, 5, 5, 1, 1, 3, 11, 1, 3, 1, 11, 1, 3, 3, 1, 9, 5, 1, 5, 1, 3, 14, 1, 3, 3, 1, 1, 5, 1, 11, 1, 9, 1, 3, 3, 2, 3, 3, 1, 15, 1, 5, 5, 1, 1, 20, 3, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A number's prime multiplicities are also called its (unsorted) prime signature. LINKS EXAMPLE The a(57) = 14 factorizations of 96 together with the corresponding multiset partitions of {1,1,1,1,1,2}:   (2*2*2*2*2*3)  {{1}{1}{1}{1}{1}{2}}   (2*2*2*3*4)    {{1}{1}{1}{2}{11}}   (2*2*2*12)     {{1}{1}{1}{112}}   (2*2*3*8)      {{1}{1}{2}{111}}   (2*2*24)       {{1}{1}{1112}}   (2*3*4*4)      {{1}{2}{11}{11}}   (2*3*16)       {{1}{2}{1111}}   (2*4*12)       {{1}{11}{112}}   (2*48)         {{1}{11112}}   (3*4*8)        {{2}{11}{111}}   (3*32)         {{2}{11111}}   (4*24)         {{11}{1112}}   (8*12)         {{111}{112}}   (96)           {{111112}} MATHEMATICA nn=100; facsusing[s_, n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facsusing[Select[s, Divisible[n/d, #]&], n/d], Min@@#>=d&]], {d, Select[s, Divisible[n, #]&]}]]; y=Select[Range[nn], UnsameQ@@Last/@FactorInteger[#]&]; Table[Length[facsusing[Rest[y], n]], {n, y}] CROSSREFS See link for additional cross-references. Cf. A098859, A112798, A130091, A255231. Sequence in context: A141110 A325758 A280073 * A190770 A292149 A275676 Adjacent sequences:  A327520 A327521 A327522 * A327524 A327525 A327526 KEYWORD nonn AUTHOR Gus Wiseman, Sep 16 2019 STATUS approved

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Last modified June 20 11:49 EDT 2021. Contains 345164 sequences. (Running on oeis4.)