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.
We define a pattern to be a finite sequence covering an initial interval of positive integers. Patterns are counted by A000670 and ranked by A333217. A sequence S is said to match a pattern P if there is a not necessarily contiguous subsequence of S whose parts have the same relative order as P. For example, (3,1,1,3) matches (1,1,2), (2,1,1), and (2,1,2), but avoids (1,2,1), (1,2,2), and (2,2,1).
LINKS
EXAMPLE
The a(n) permutations for n = 1, 6, 12, 24, 30, 36, 60, 72, 120:
() (12) (112) (1112) (132) (1122) (1132) (11122) (11132)
(21) (121) (1121) (213) (1212) (1312) (11212) (11312)
(211) (1211) (231) (1221) (1321) (11221) (11321)
(2111) (312) (2112) (2113) (12112) (13112)
(321) (2121) (2131) (12121) (13121)
(2211) (2311) (12211) (13211)
(3112) (21112) (21113)
(3121) (21121) (21131)
(3211) (21211) (21311)
(22111) (23111)
(31112)
(31121)
(31211)
(32111)
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[Select[Permutations[primeMS[n]], !MatchQ[#, {___, x_, ___, y_, ___, z_, ___}/; x<y<z]&]], {n, 100}]
CROSSREFS
These compositions are counted by A102726.
Patterns avoiding this pattern are counted by A226316.
The complement A335520 is the matching version.
Permutations of prime indices are counted by A008480.
Anti-run permutations of prime indices are counted by A335452.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 19 2020
STATUS
approved