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 A319118 Number of multimin tree-factorizations of n. 3
 1, 1, 1, 2, 1, 2, 1, 6, 2, 2, 1, 8, 1, 2, 2, 24, 1, 6, 1, 8, 2, 2, 1, 42, 2, 2, 6, 8, 1, 8, 1, 112, 2, 2, 2, 38, 1, 2, 2, 42, 1, 8, 1, 8, 8, 2, 1, 244, 2, 6, 2, 8, 1, 24, 2, 42, 2, 2, 1, 58, 1, 2, 8, 568, 2, 8, 1, 8, 2, 8, 1, 268, 1, 2, 6, 8, 2, 8, 1, 244, 24 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A multimin factorization of n is an ordered factorization of n into factors greater than 1 such that the sequence of minimal primes dividing each factor is weakly increasing. A multimin tree-factorization of n is either the number n itself or a sequence of multimin tree-factorizations, one of each factor in a multimin factorization of n with at least two factors. LINKS FORMULA a(prime^n) = A118376(n). a(product of n distinct primes) = A005804(n). EXAMPLE The a(12) = 8 multimin tree-factorizations: 12, (2*6), (4*3), (6*2), (2*2*3), (2*(2*3)), ((2*2)*3), ((2*3)*2). Or as series-reduced plane trees of multisets: 112, (1,12), (11,2), (12,1), (1,1,2), (1,(1,2)), ((1,1),2)), ((1,2),1). MATHEMATICA facs[n_]:=If[n<=1, {{}}, Join@@Table[(Prepend[#1, d]&)/@Select[facs[n/d], Min@@#1>=d&], {d, Rest[Divisors[n]]}]]; mmftrees[n_]:=Prepend[Join@@(Tuples[mmftrees/@#]&/@Select[Join@@Permutations/@Select[facs[n], Length[#]>1&], OrderedQ[FactorInteger[#][[1, 1]]&/@#]&]), n]; Table[Length[mmftrees[n]], {n, 100}] CROSSREFS Cf. A001055, A005804, A020639, A118376, A196545, A255397, A281113, A281118, A281119, A295279, A317545, A317546, A318577, A319119. Sequence in context: A205405 A112623 A130675 * A163820 A284465 A327899 Adjacent sequences: A319115 A319116 A319117 * A319119 A319120 A319121 KEYWORD nonn AUTHOR Gus Wiseman, Sep 10 2018 STATUS approved

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Last modified January 29 11:27 EST 2023. Contains 359922 sequences. (Running on oeis4.)