cp's OEIS Frontend

A335127 A multiset whose multiplicities are the prime indices of n is separable.

%I A335127 #9 Jul 03 2020 06:58:37
%S A335127 1,2,4,6,8,9,12,15,16,18,20,24,25,27,30,32,35,36,40,42,45,48,49,50,54,
%T A335127 56,60,63,64,70,72,75,77,80,81,84,90,96,98,99,100,105,108,110,112,120,
%U A335127 121,125,126,128,132,135,140,143,144,147,150,154,160,162,165
%N A335127 A multiset whose multiplicities are the prime indices of n is separable.
%C A335127 A multiset is separable if it has a permutation that is an anti-run, meaning there are no adjacent equal parts.
%C A335127 A multiset whose multiplicities are the prime indices of n (such as row n of A305936) is not the same as the multiset of prime indices of n. For example, the prime indices of 12 are {1,1,2}, while a multiset whose multiplicities are {1,1,2} is {1,1,2,3}.
%e A335127 The sequence together with the corresponding multisets begins:
%e A335127    1: {}
%e A335127    2: {1}
%e A335127    4: {1,2}
%e A335127    6: {1,1,2}
%e A335127    8: {1,2,3}
%e A335127    9: {1,1,2,2}
%e A335127   12: {1,1,2,3}
%e A335127   15: {1,1,1,2,2}
%e A335127   16: {1,2,3,4}
%e A335127   18: {1,1,2,2,3}
%e A335127   20: {1,1,1,2,3}
%e A335127   24: {1,1,2,3,4}
%e A335127   25: {1,1,1,2,2,2}
%e A335127   27: {1,1,2,2,3,3}
%e A335127   30: {1,1,1,2,2,3}
%t A335127 nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A335127 Select[Range[100],Select[Permutations[nrmptn[#]],!MatchQ[#,{___,x_,x_,___}]&]!={}&]
%Y A335127 The complement is A335126.
%Y A335127 Anti-run compositions are A003242.
%Y A335127 Anti-runs are ranked by A333489.
%Y A335127 Separable partitions are A325534.
%Y A335127 Inseparable partitions are A325535.
%Y A335127 Separable factorizations are A335434.
%Y A335127 Inseparable factorizations are A333487.
%Y A335127 Separable partitions are ranked by A335433.
%Y A335127 Inseparable partitions are ranked by A335448.
%Y A335127 Anti-run permutations of prime indices are A335452.
%Y A335127 Patterns contiguously matched by compositions are A335457.
%Y A335127 Cf. A056239, A106351, A112798, A114938, A292884, A335489, A335516, A335838.
%K A335127 nonn
%O A335127 1,2
%A A335127 _Gus Wiseman_, Jul 02 2020