OFFSET
1,6
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
A sequence of integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
Also permutations of the multiset of prime indices of n avoiding the patterns (2,1,2), (2,1,3), and (3,1,2).
LINKS
EXAMPLE
The a(n) permutations for n = 2, 6, 12, 24, 48, 60, 120, 180:
(1) (12) (112) (1112) (11112) (1123) (11123) (11223)
(21) (121) (1121) (11121) (1132) (11132) (11232)
(211) (1211) (11211) (1231) (11231) (11322)
(2111) (12111) (1321) (11321) (12231)
(21111) (2311) (12311) (12321)
(3211) (13211) (13221)
(23111) (22311)
(32111) (23211)
(32211)
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {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[primeMS[n]], unimodQ]], {n, 30}]
CROSSREFS
Dominated by A008480.
A more interesting version is A332294.
The complement is counted by A332671.
Unimodal compositions are A001523.
Unimodal normal sequences appear to be A007052.
Unimodal permutations are A011782.
Non-unimodal permutations are A059204.
Numbers with non-unimodal unsorted prime signature are A332282.
Partitions with unimodal 0-appended first differences are A332283.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 22 2020
STATUS
approved