OFFSET
1,4
COMMENTS
This multiset is generally 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}.
A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
LINKS
MathWorld, Unimodal Sequence
EXAMPLE
The a(12) = 6 permutations:
{1,1,2,3}
{1,1,3,2}
{1,2,3,1}
{1,3,2,1}
{2,3,1,1}
{3,2,1,1}
MATHEMATICA
nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]], {#1}]&, If[n==1, {}, Flatten[Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]]]];
unimodQ[q_]:=Or[Length[q]<=1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]];
Table[Length[Select[Permutations[nrmptn[n]], unimodQ]], {n, 0, 30}]
CROSSREFS
Dominated by A318762.
A less interesting version is A332288.
The complement is counted by A332672.
The opposite/negative version is A332741.
Unimodal compositions are A001523.
Non-unimodal permutations are A059204.
Partitions whose run-lengths are unimodal are A332280.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 21 2020
STATUS
approved