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 A281113 Number of twice-factorizations of n. Number of ways to choose a postpositive factorization of each part of a postpositive factorization of n. 89
 1, 1, 3, 1, 3, 1, 6, 3, 3, 1, 9, 1, 3, 3, 15, 1, 9, 1, 9, 3, 3, 1, 23, 3, 3, 6, 9, 1, 12, 1, 28, 3, 3, 3, 32, 1, 3, 3, 23, 1, 12, 1, 9, 9, 3, 1, 58, 3, 9, 3, 9, 1, 23, 3, 23, 3, 3, 1, 41, 1, 3, 9, 66, 3, 12, 1, 9, 3, 12, 1, 84, 1, 3, 9, 9, 3, 12, 1, 58, 15, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS A postpositive number is a positive integer other than 1. A postpositive factorization of n is a finite orderless sequence of postpositive numbers whose product is n. LINKS Michael De Vlieger, Table of n, a(n) for n = 2..30030 Michael De Vlieger, Indices of records in A281113. EXAMPLE The a(20)=9 twice-factorizations are: ((20)), ((2*10)), ((4*5)), ((2*2*5)), ((2)*(10)), ((2)*(2*5)), ((4)*(5)), ((2*2)*(5)), ((2)*(2)*(5)). Twice-factorizations of 32 organized by composite: ((2)(2)(2)(2)(2)) ((2)(2)(2)(2 2)) ((2)(2)(2 2 2)) ((2)(2 2)(2 2)) ((2)(2 2 2 2)) ((2 2)(2 2 2)) ((2 2 2 2 2)) ((2)(2)(2)(4))    ((2)(2)(2 4))    ((2)(2 2)(4))   ((2)(4)(2 2))   ((2)(2 2 4))   ((2 2)(2 4))   ((4)(2 2 2))  ((2 2 2 4)) ((2)(2)(8))       ((2)(2 8))       ((2 2)(8))      ((2 2 8)) ((2)(4)(4))       ((2)(4 4))       ((4)(2 4))      ((2 4 4)) ((2)(16))         ((2 16)) ((4)(8))          ((4 8)) ((32)). Twice-factorizations of 32 organized by domain: ((2)(2)(2)(2)(2)) ((2)(2)(2)(2 2)) ((2)(2)(2)(4)) ((2)(2)(2 2 2))  ((2)(2)(2 4)) ((2)(2)(8)) ((2)(2 2)(2 2))  ((2)(2 2)(4)) ((2)(4)(2 2)) ((2)(4)(4)) ((2)(2 2 2 2))   ((2)(2 2 4))  ((2)(2 8))    ((2)(4 4))   ((2)(16)) ((2 2)(2 2 2))   ((2 2)(2 4))  ((2 2)(8))    ((4)(2 2 2)) ((4)(2 4)) ((4)(8)) ((2 2 2 2 2))    ((2 2 2 4))   ((2 2 8))     ((2 4 4))    ((2 16))   ((4 8)) ((32)). MATHEMATICA postfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[postfacs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; twicefacs[n_]:=Join@@Tuples/@Map[postfacs, postfacs[n], {2}]; Table[Length[twicefacs[n]], {n, 2, 24}] CROSSREFS Cf. A001055(n) = number of factorizations of n, A050336(n) = number of orderless twice-factorizations of n, A162247(n) = factors of factorizations of n, A063834(n) = a(p^(n-1)), A007716, A269134, A281116. Sequence in context: A066637 A317144 A050336 * A236757 A095250 A135521 Adjacent sequences:  A281110 A281111 A281112 * A281114 A281115 A281116 KEYWORD nonn AUTHOR Gus Wiseman, Jan 14 2017 STATUS approved

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Last modified September 21 14:54 EDT 2020. Contains 337272 sequences. (Running on oeis4.)