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 A327400 Number of factorizations of n that are constant or whose factors are relatively prime. 3
 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 2, 3, 1, 5, 1, 2, 2, 2, 2, 7, 1, 2, 2, 4, 1, 5, 1, 3, 3, 2, 1, 6, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 9, 1, 2, 3, 4, 2, 5, 1, 3, 2, 5, 1, 10, 1, 2, 3, 3, 2, 5, 1, 6, 3, 2, 1, 9, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS First differs from A327399 at a(24) = 4, A327399(24) = 3. LINKS FORMULA a(n) = A281116(n) + A089723(n). EXAMPLE The factorizations of 2, 4, 12, 24, 30, 36, 48, and 60 that are constant or whose factors are relatively prime:   2   4     12      24        30      36        48          60       2*2   3*4     3*8       5*6     4*9       3*16        3*20             2*2*3   2*3*4     2*15    6*6       2*3*8       4*15                     2*2*2*3   3*10    2*2*9     3*4*4       5*12                               2*3*5   2*3*6     2*2*3*4     2*5*6                                       3*3*4     2*2*2*2*3   3*4*5                                       2*2*3*3               2*2*15                                                             2*3*10                                                             2*2*3*5 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||GCD@@#==1&]], {n, 100}] CROSSREFS Constant factorizations are A089723. Cf. A007359, A051424, A281116, A302569, A304709, A304711, A319269, A327399. Sequence in context: A320732 A305149 A336737 * A323303 A068108 A342679 Adjacent sequences:  A327397 A327398 A327399 * A327401 A327402 A327403 KEYWORD nonn AUTHOR Gus Wiseman, Sep 22 2019 STATUS approved

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Last modified July 31 23:46 EDT 2021. Contains 346377 sequences. (Running on oeis4.)