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 A327399 Number of factorizations of n that are constant or whose distinct factors are pairwise coprime. 3
 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 3, 2, 2, 2, 3, 1, 5, 1, 2, 2, 2, 2, 6, 1, 2, 2, 3, 1, 5, 1, 3, 3, 2, 1, 4, 2, 3, 2, 3, 1, 3, 2, 3, 2, 2, 1, 7, 1, 2, 3, 4, 2, 5, 1, 3, 2, 5, 1, 5, 1, 2, 3, 3, 2, 5, 1, 4, 3, 2, 1, 7, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS First differs from A327400 at A327400(24) = 4, a(24) = 3. LINKS FORMULA a(n) = A327695(n) + A089723(n). EXAMPLE The a(90) = 7 factorizations together with the corresponding multiset partitions of {1,2,2,3}:   (2*3*3*5)  {{1},{2},{2},{3}}   (2*5*9)    {{1},{3},{2,2}}   (2*45)     {{1},{2,2,3}}   (3*3*10)   {{2},{2},{1,3}}   (5*18)     {{3},{1,2,2}}   (9*10)     {{2,2},{1,3}}   (90)       {{1,2,2,3}} 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], Length[Union[#]]==1||CoprimeQ@@Union[#]&]], {n, 100}] CROSSREFS Constant factorizations are A089723. Partitions whose distinct parts are pairwise coprime are A304709. Factorizations that are constant or relatively prime are A327400. See link for additional cross-references. A007359, A050320, A051424, A281116, A302569, A302696, A304711. Sequence in context: A076755 A317751 A106490 * A122375 A038548 A320732 Adjacent sequences:  A327396 A327397 A327398 * A327400 A327401 A327402 KEYWORD nonn AUTHOR Gus Wiseman, Sep 22 2019 STATUS approved

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Last modified May 18 18:33 EDT 2021. Contains 343998 sequences. (Running on oeis4.)