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 A330936 Number of nontrivial factorizations of n into factors > 1. 3
 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 2, 0, 2, 0, 0, 0, 5, 0, 0, 1, 2, 0, 3, 0, 5, 0, 0, 0, 7, 0, 0, 0, 5, 0, 3, 0, 2, 2, 0, 0, 10, 0, 2, 0, 2, 0, 5, 0, 5, 0, 0, 0, 9, 0, 0, 2, 9, 0, 3, 0, 2, 0, 3, 0, 14, 0, 0, 2, 2, 0, 3, 0, 10, 3, 0, 0, 9, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 COMMENTS The trivial factorizations of a number are (1) the case with only one factor, and (2) the factorization into prime numbers. LINKS FORMULA For prime n, a(n) = 0; for nonprime n, a(n) = A001055(n) - 2. EXAMPLE The a(n) nontrivial factorizations of n = 8, 12, 16, 24, 36, 48, 60, 72:   (2*4)  (2*6)  (2*8)    (3*8)    (4*9)    (6*8)      (2*30)    (8*9)          (3*4)  (4*4)    (4*6)    (6*6)    (2*24)     (3*20)    (2*36)                 (2*2*4)  (2*12)   (2*18)   (3*16)     (4*15)    (3*24)                          (2*2*6)  (3*12)   (4*12)     (5*12)    (4*18)                          (2*3*4)  (2*2*9)  (2*3*8)    (6*10)    (6*12)                                   (2*3*6)  (2*4*6)    (2*5*6)   (2*4*9)                                   (3*3*4)  (3*4*4)    (3*4*5)   (2*6*6)                                            (2*2*12)   (2*2*15)  (3*3*8)                                            (2*2*2*6)  (2*3*10)  (3*4*6)                                            (2*2*3*4)            (2*2*18)                                                                 (2*3*12)                                                                 (2*2*2*9)                                                                 (2*2*3*6)                                                                 (2*3*3*4) MATHEMATICA facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; Table[Length[DeleteCases[Rest[facs[n]], {_}]], {n, 100}] CROSSREFS Positions of nonzero terms are A033942. Positions of 1's are A030078. Positions of 2's are A054753. Nontrivial integer partitions are A007042. Nontrivial set partitions are A008827. Nontrivial divisors are A070824. Cf. A001055, A003238, A005121, A317145, A317176, A318812, A330665, A330935. Sequence in context: A262889 A083059 A173440 * A284687 A046268 A202425 Adjacent sequences:  A330933 A330934 A330935 * A330938 A330939 A330940 KEYWORD nonn AUTHOR Gus Wiseman, Jan 04 2020 STATUS approved

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Last modified February 18 12:34 EST 2020. Contains 332018 sequences. (Running on oeis4.)