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 A296120 Number of ways to choose a strict factorization of each factor in a strict factorization of n. 6
 1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 6, 1, 3, 3, 4, 1, 6, 1, 6, 3, 3, 1, 13, 1, 3, 3, 6, 1, 12, 1, 7, 3, 3, 3, 14, 1, 3, 3, 13, 1, 12, 1, 6, 6, 3, 1, 25, 1, 6, 3, 6, 1, 13, 3, 13, 3, 3, 1, 31, 1, 3, 6, 11, 3, 12, 1, 6, 3, 12, 1, 36, 1, 3, 6, 6, 3, 12, 1, 25, 4, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS Table of n, a(n) for n=1..82. FORMULA Dirichlet g.f.: Product_{n > 1}(1 + A045778(n)/n^s). EXAMPLE The a(36) = 14 twice-factorizations: (36), (4*9), (3*12), (2*18), (2*3*6), (4)*(9), (3)*(12), (3)*(3*4), (3)*(2*6), (2)*(18), (2)*(3*6), (2)*(2*9), (2)*(3)*(6), (2)*(3)*(2*3). MATHEMATICA sfs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[sfs[n/d], Min@@#>d&]], {d, Rest[Divisors[n]]}]]; Table[Sum[Times@@Length/@sfs/@fac, {fac, sfs[n]}], {n, 100}] CROSSREFS Cf. A000009, A005117, A045778, A050345, A279785, A281113, A294788, A296118, A296119, A296121. Sequence in context: A294788 A254578 A348610 * A050345 A348611 A070039 Adjacent sequences: A296117 A296118 A296119 * A296121 A296122 A296123 KEYWORD nonn AUTHOR Gus Wiseman, Dec 05 2017 STATUS approved

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Last modified September 30 21:59 EDT 2023. Contains 365812 sequences. (Running on oeis4.)