This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A318577 #13 Sep 11 2018 17:01:11
%S A318577 0,1,1,1,1,1,1,3,1,1,1,4,1,1,1,11,1,3,1,4,1,1,1,19,1,1,3,4,1,4,1,45,1,
%T A318577 1,1,17,1,1,1,19,1,4,1,4,4,1,1,96,1,3,1,4,1,11,1,19,1,1,1,26,1,1,4,
%U A318577 197,1,4,1,4,1,4,1,104,1,1,3,4,1,4,1,96,11,1,1,26,1,1,1,19,1,19,1,4,1,1,1,501,1,3,4,17
%N A318577 Number of complete multimin tree-factorizations of n.
%C A318577 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 at least two multimin tree-factorizations, one of each factor in a multimin factorization of n. A multimin tree-factorization is complete if the leaves are all prime numbers.
%F A318577 a(prime^n) = A001003(n - 1).
%F A318577 a(product of n distinct primes) = A000311(n).
%e A318577 The a(12) = 4 trees are (2*2*3), (2*(2*3)), ((2*3)*2), ((2*2)*3).
%t A318577 facs[n_]:=If[n<=1,{{}},Join@@Table[(Prepend[#1,d]&)/@Select[facs[n/d],Min@@#1>=d&],{d,Rest[Divisors[n]]}]];
%t A318577 mmftrees[n_]:=Prepend[Join@@(Tuples[mmftrees/@#]&/@Select[Join@@Permutations/@Select[facs[n],Length[#]>1&],OrderedQ[FactorInteger[#][[1,1]]&/@#]&]),n];
%t A318577 Table[Length[Select[mmftrees[n],FreeQ[#,_Integer?(!PrimeQ[#]&)]&]],{n,100}]
%Y A318577 Cf. A000311, A001003, A001055, A020639, A255397, A281113, A281118, A281119, A295281, A317545, A319118, A319121.
%K A318577 nonn
%O A318577 1,8
%A A318577 _Gus Wiseman_, Sep 11 2018