This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335521 #7 Jun 30 2020 01:54:55
%S A335521 1,1,1,1,1,2,1,1,1,2,1,3,1,2,2,1,1,3,1,3,2,2,1,4,1,2,1,3,1,5,1,1,2,2,
%T A335521 2,6,1,2,2,4,1,5,1,3,3,2,1,5,1,3,2,3,1,4,2,4,2,2,1,9,1,2,3,1,2,5,1,3,
%U A335521 2,5,1,10,1,2,3,3,2,5,1,5,1,2,1,9,2,2,2
%N A335521 Number of (1,2,3)-avoiding permutations of the prime indices of n.
%C A335521 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.
%C A335521 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).
%H A335521 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335521 Gus Wiseman, <a href="https://oeis.org/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%F A335521 For n > 0, a(n) + A335520(n) = A008480(n).
%e A335521 The a(n) permutations for n = 1, 6, 12, 24, 30, 36, 60, 72, 120:
%e A335521 () (12) (112) (1112) (132) (1122) (1132) (11122) (11132)
%e A335521 (21) (121) (1121) (213) (1212) (1312) (11212) (11312)
%e A335521 (211) (1211) (231) (1221) (1321) (11221) (11321)
%e A335521 (2111) (312) (2112) (2113) (12112) (13112)
%e A335521 (321) (2121) (2131) (12121) (13121)
%e A335521 (2211) (2311) (12211) (13211)
%e A335521 (3112) (21112) (21113)
%e A335521 (3121) (21121) (21131)
%e A335521 (3211) (21211) (21311)
%e A335521 (22111) (23111)
%e A335521 (31112)
%e A335521 (31121)
%e A335521 (31211)
%e A335521 (32111)
%t A335521 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A335521 Table[Length[Select[Permutations[primeMS[n]],!MatchQ[#,{___,x_,___,y_,___,z_,___}/;x<y<z]&]],{n,100}]
%Y A335521 These compositions are counted by A102726.
%Y A335521 Patterns avoiding this pattern are counted by A226316.
%Y A335521 The complement A335520 is the matching version.
%Y A335521 Permutations of prime indices are counted by A008480.
%Y A335521 Patterns are counted by A000670 and ranked by A333217.
%Y A335521 Anti-run permutations of prime indices are counted by A335452.
%Y A335521 Cf. A056239, A056986, A112798, A238279, A281188, A333221, A333755, A335456, A335460, A335462, A335463.
%K A335521 nonn
%O A335521 1,6
%A A335521 _Gus Wiseman_, Jun 19 2020