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 A335450 #10 Jun 29 2020 22:21:36
%S A335450 1,1,1,1,1,2,1,1,1,2,1,3,1,2,2,1,1,2,1,3,2,2,1,4,1,2,1,3,1,6,1,1,2,2,
%T A335450 2,3,1,2,2,4,1,6,1,3,3,2,1,5,1,2,2,3,1,2,2,4,2,2,1,12,1,2,3,1,2,6,1,3,
%U A335450 2,6,1,4,1,2,2,3,2,6,1,5,1,2,1,12,2,2
%N A335450 Number of (2,1,2)-avoiding permutations of the prime indices of n.
%C A335450 Depends only on unsorted prime signature (A124010), but not only on sorted prime signature (A118914).
%C A335450 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 A335450 We define a pattern to be a finite sequence covering an initial interval of positive integers. Patterns are counted by A000670. 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 A335450 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335450 Gus Wiseman, <a href="/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%e A335450 The permutations for n = 2, 6, 12, 24, 30, 48, 60, 90:
%e A335450 (1) (12) (112) (1112) (123) (11112) (1123) (1223)
%e A335450 (21) (211) (2111) (132) (21111) (1132) (1322)
%e A335450 (213) (2113) (2123)
%e A335450 (231) (2311) (2213)
%e A335450 (312) (3112) (2231)
%e A335450 (321) (3211) (3122)
%e A335450 (3212)
%e A335450 (3221)
%t A335450 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A335450 Table[Length[Select[Permutations[primeMS[n]],!MatchQ[#,{___,x_,___,y_,___,x_,___}/;x>y]&]],{n,100}]
%Y A335450 Positions of ones are A000961.
%Y A335450 Replacing (2,1,2) with (1,2,1) gives A335449.
%Y A335450 The matching version is A335453.
%Y A335450 Patterns are counted by A000670.
%Y A335450 (2,1,2)-avoiding patterns are counted by A001710.
%Y A335450 Permutations of prime indices are counted by A008480.
%Y A335450 Unsorted prime signature is A124010. Sorted prime signature is A118914.
%Y A335450 (1,2,1) and (2,1,2)-avoiding permutations of prime indices are A333175.
%Y A335450 STC-numbers of permutations of prime indices are A333221.
%Y A335450 (1,2,1) and (2,1,2)-avoiding permutations of prime indices are A335448.
%Y A335450 Patterns matched by standard compositions are counted by A335454.
%Y A335450 (1,2,1) or (2,1,2)-matching permutations of prime indices are A335460.
%Y A335450 (1,2,1) and (2,1,2)-matching permutations of prime indices are A335462.
%Y A335450 Dimensions of downsets of standard compositions are A335465.
%Y A335450 (2,1,2)-avoiding compositions are ranked by A335469.
%Y A335450 (2,1,2)-avoiding compositions are counted by A335473.
%Y A335450 (2,2,1)-avoiding compositions are ranked by A335524.
%Y A335450 (1,2,2)-avoiding compositions are ranked by A335525.
%Y A335450 Cf. A056239, A056986, A112798, A158005, A181796, A335452, A335463.
%K A335450 nonn
%O A335450 1,6
%A A335450 _Gus Wiseman_, Jun 14 2020