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 A296132 Number of twice-factorizations of n where the first factorization is constant and the latter factorizations are strict, i.e., type (P,R,Q). 6
 1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 5, 2, 2, 3, 3, 1, 5, 1, 4, 2, 2, 2, 9, 1, 2, 2, 5, 1, 5, 1, 3, 3, 2, 1, 7, 2, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 9, 1, 2, 3, 10, 2, 5, 1, 3, 2, 5, 1, 9, 1, 2, 3, 3, 2, 5, 1, 7, 4, 2, 1, 9, 2, 2, 2 (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 d|n and then a sequence of log_d(n) strict factorizations of d. LINKS EXAMPLE The a(36) = 9 twice-factorizations are (2*3)*(2*3), (2*3)*(6), (6)*(2*3), (6)*(6), (2*3*6), (2*18), (3*12), (4*9), (36). MATHEMATICA sfs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[sfs[n/d], Min@@#>d&]], {d, Rest[Divisors[n]]}]]; Table[Sum[Length[sfs[n^(1/g)]]^g, {g, Divisors[GCD@@FactorInteger[n][[All, 2]]]}], {n, 100}] CROSSREFS Cf. A000005, A001055, A005117, A045778, A052409, A052410, A089723, A279788, A281113, A284639, A295920, A295931. Sequence in context: A257091 A319269 A320888 * A253557 A098893 A302037 Adjacent sequences:  A296129 A296130 A296131 * A296133 A296134 A296135 KEYWORD nonn AUTHOR Gus Wiseman, Dec 05 2017 STATUS approved

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Last modified January 16 13:32 EST 2019. Contains 319193 sequences. (Running on oeis4.)