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 A327658 Number of factorizations of n that are empty or whose factors have a common divisor > 1. 3
 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 5, 1, 2, 1, 2, 1, 1, 1, 4, 2, 1, 3, 2, 1, 1, 1, 7, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 1, 7, 2, 2, 1, 2, 1, 4, 1, 4, 1, 1, 1, 3, 1, 1, 2, 11, 1, 1, 1, 2, 1, 1, 1, 7, 1, 1, 2, 2, 1, 1, 1, 7, 5, 1, 1, 3, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS First differs from A319786 at a(900) = 11, A319786(900) = 12. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. Numbers whose prime indices have a common divisor > 1 are listed in A318978. LINKS EXAMPLE The a(120) = 7 factorizations:   (120)   (2*60)   (4*30)   (6*20)   (10*12)   (2*2*30)   (2*6*10) 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], #=={}||GCD@@#!=1&]], {n, 100}] CROSSREFS See link for additional cross-references. Cf. A000005, A056239, A112798, A281116, A289509, A327406. Sequence in context: A322453 A327012 A328855 * A319786 A321271 A305193 Adjacent sequences:  A327655 A327656 A327657 * A327659 A327660 A327661 KEYWORD nonn AUTHOR Gus Wiseman, Sep 21 2019 STATUS approved

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Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)