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 A296121 Number of twice-factorizations of n with no repeated factorizations. 5
 1, 1, 1, 2, 1, 3, 1, 5, 2, 3, 1, 8, 1, 3, 3, 10, 1, 8, 1, 8, 3, 3, 1, 20, 2, 3, 5, 8, 1, 12, 1, 20, 3, 3, 3, 25, 1, 3, 3, 20, 1, 12, 1, 8, 8, 3, 1, 47, 2, 8, 3, 8, 1, 20, 3, 20, 3, 3, 1, 38, 1, 3, 8, 40, 3, 12, 1, 8, 3, 12, 1, 68, 1, 3, 8, 8, 3, 12, 1, 47, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS From Robert G. Wilson v, Dec 05 2017: (Start) a(n) = 1 iff n equals 1 or is a prime; a(n) = 2 iff n is a prime squared; a(n) = 3 iff n is a squarefree semiprime; a(n) = 5 iff n is a prime cube; a(n) = 8 iff n is of the form p^2*q, etc. (End) LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..1000 EXAMPLE The a(12) = 8 twice-factorizations: (2)*(2*3), (3)*(2*2), (2*2*3), (2)*(6), (2*6), (3)*(4), (3*4), (12). MATHEMATICA facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; Table[Length[Join@@Table[Select[Tuples[facs/@p], UnsameQ@@#&], {p, facs[n]}]], {n, 100}] CROSSREFS Cf. A001055, A045778, A050345, A063834, A089723, A281113, A296118, A296119, A296120, A296122. Sequence in context: A278136 A085053 A296118 * A277120 A104725 A289079 Adjacent sequences: A296118 A296119 A296120 * A296122 A296123 A296124 KEYWORD nonn AUTHOR Gus Wiseman, Dec 05 2017 STATUS approved

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Last modified September 27 01:21 EDT 2023. Contains 365669 sequences. (Running on oeis4.)