cp's OEIS Frontend

A333487 Number of inseparable factorizations of n into factors > 1.

%I A333487 #6 Jul 01 2020 22:30:16
%S A333487 0,0,0,1,0,0,0,1,1,0,0,0,0,0,0,2,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,2,0,0,
%T A333487 0,1,0,0,0,1,0,0,0,0,0,0,0,2,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,5,0,0,0,0,
%U A333487 0,0,0,1,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0
%N A333487 Number of inseparable factorizations of n into factors > 1.
%C A333487 A multiset is separable if it has a permutation that is an anti-run, meaning there are no adjacent equal parts.
%F A333487 a(n) + A335434(n) = A001055(n).
%e A333487 The a(n) factorizations for n = 4, 16, 96, 144, 64, 192:
%e A333487   2*2  4*4      2*2*2*12     12*12        8*8          3*4*4*4
%e A333487        2*2*2*2  2*2*2*2*6    2*2*2*18     4*4*4        2*2*2*24
%e A333487                 2*2*2*2*2*3  2*2*2*2*9    2*2*2*8      2*2*2*2*12
%e A333487                              2*2*2*2*3*3  2*2*2*2*4    2*2*2*2*2*6
%e A333487                                           2*2*2*2*2*2  2*2*2*2*3*4
%e A333487                                                        2*2*2*2*2*2*3
%t A333487 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A333487 Table[Length[Select[facs[n],Select[Permutations[#],!MatchQ[#,{___,x_,x_,___}]&]=={}&]],{n,100}]
%Y A333487 The version for partitions is A325535.
%Y A333487 The version for multisets with prescribed multiplicities is A335126.
%Y A333487 The separable version is A335434.
%Y A333487 Anti-run compositions are A003242.
%Y A333487 Anti-runs are ranked by A333489.
%Y A333487 Separable partitions are ranked by A335433.
%Y A333487 Inseparable partitions are ranked by A335448.
%Y A333487 Anti-run permutations of prime indices are A335452.
%Y A333487 Patterns contiguously matched by compositions are A335457.
%Y A333487 Cf. A106351, A292884, A295370, A333628, A333755, A335463, A335125, A335127, A335407, A335474, A335516, A335838.
%K A333487 nonn
%O A333487 1,16
%A A333487 _Gus Wiseman_, Jul 01 2020