OFFSET
1,8
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 integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
LINKS
Eric Weisstein's World of Mathematics, Unimodal Sequence
EXAMPLE
The a(n) permutations for n = 6, 8, 9, 10, 12, 14, 15, 16:
121 132 1212 1121 1132 11121 11212 1243
231 1221 1211 1213 11211 11221 1324
2121 1231 12111 12112 1342
1312 12121 1423
1321 12211 1432
2131 21121 2143
2311 21211 2314
3121 2341
2413
2431
3142
3241
3412
3421
4132
4231
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, 30}]
CROSSREFS
Dominated by A318762.
The complement of the non-negated version is counted by A332294.
The non-negated version is A332672.
The complement is counted by A332741.
A less interesting version is A333146.
Unimodal compositions are A001523.
Unimodal normal sequences are A007052.
Non-unimodal normal sequences are A328509.
Partitions with non-unimodal 0-appended first differences are A332284.
Compositions whose negation is unimodal are A332578.
Partitions with non-unimodal negated run-lengths are A332639.
Numbers whose negated prime signature is not unimodal are A332642.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 09 2020
STATUS
approved