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 A295935 Number of twice-factorizations of n where the latter factorizations are constant, i.e., type (P,P,R). 17
 1, 1, 1, 3, 1, 2, 1, 5, 3, 2, 1, 5, 1, 2, 2, 12, 1, 5, 1, 5, 2, 2, 1, 10, 3, 2, 5, 5, 1, 5, 1, 18, 2, 2, 2, 15, 1, 2, 2, 10, 1, 5, 1, 5, 5, 2, 1, 22, 3, 5, 2, 5, 1, 10, 2, 10, 2, 2, 1, 13, 1, 2, 5, 40, 2, 5, 1, 5, 2, 5, 1, 28, 1, 2, 5, 5, 2, 5, 1, 22, 12, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) is also the number of ways to choose a perfect divisor of each factor in a factorization of n. LINKS FORMULA Dirichlet g.f.: 1/Product_{n > 1}(1 - A089723(n)/n^s). EXAMPLE The a(24) = 10 twice-factorizations are: (2)*(2)*(2)*(3), (2)*(3)*(2*2), (3)*(2*2*2) (2)*(2)*(6), (2*2)*(6), (2)*(3)*(4), (2)*(12), (3)*(8), (4)*(6), (24). MATHEMATICA facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; Table[Sum[Product[Length[Divisors[GCD@@FactorInteger[d][[All, 2]]]], {d, f}], {f, facs[n]}], {n, 100}] CROSSREFS Cf. A000005, A001055, A052409, A052410, A089723, A279784, A281113, A284639, A295923, A295924, A295931. Sequence in context: A214208 A279965 A285121 * A318323 A347396 A135261 Adjacent sequences: A295932 A295933 A295934 * A295936 A295937 A295938 KEYWORD nonn AUTHOR Gus Wiseman, Nov 29 2017 STATUS approved

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Last modified December 9 00:20 EST 2022. Contains 358698 sequences. (Running on oeis4.)