OFFSET
1,2
COMMENTS
A multiset is separable if it has a permutation that is an anti-run, meaning there are no adjacent equal parts.
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}.
EXAMPLE
The sequence together with the corresponding multisets begins:
1: {}
2: {1}
4: {1,2}
6: {1,1,2}
8: {1,2,3}
9: {1,1,2,2}
12: {1,1,2,3}
15: {1,1,1,2,2}
16: {1,2,3,4}
18: {1,1,2,2,3}
20: {1,1,1,2,3}
24: {1,1,2,3,4}
25: {1,1,1,2,2,2}
27: {1,1,2,2,3,3}
30: {1,1,1,2,2,3}
MATHEMATICA
nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]], {#1}]&, If[n==1, {}, Flatten[Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]]]];
Select[Range[100], Select[Permutations[nrmptn[#]], !MatchQ[#, {___, x_, x_, ___}]&]!={}&]
CROSSREFS
The complement is A335126.
Anti-run compositions are A003242.
Anti-runs are ranked by A333489.
Separable partitions are A325534.
Inseparable partitions are A325535.
Separable factorizations are A335434.
Inseparable factorizations are A333487.
Separable partitions are ranked by A335433.
Inseparable partitions are ranked by A335448.
Anti-run permutations of prime indices are A335452.
Patterns contiguously matched by compositions are A335457.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 02 2020
STATUS
approved