cp's OEIS Frontend

A335449 Number of (1,2,1)-avoiding permutations of the prime indices of n.

%I A335449 #8 Jun 29 2020 22:21:19
%S A335449 1,1,1,1,1,2,1,1,1,2,1,2,1,2,2,1,1,3,1,2,2,2,1,2,1,2,1,2,1,6,1,1,2,2,
%T A335449 2,3,1,2,2,2,1,6,1,2,2,2,1,2,1,3,2,2,1,4,2,2,2,2,1,6,1,2,2,1,2,6,1,2,
%U A335449 2,6,1,3,1,2,3,2,2,6,1,2,1,2,1,6,2,2,2
%N A335449 Number of (1,2,1)-avoiding permutations of the prime indices of n.
%C A335449 Depends only on unsorted prime signature (A124010), but not only on sorted prime signature (A118914).
%C A335449 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 A335449 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 A335449 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335449 Gus Wiseman, <a href="/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%e A335449 The a(n) permutations for n = 2, 10, 36, 54, 324, 30, 1458, 90:
%e A335449   (1)  (13)  (1122)  (1222)  (112222)  (123)  (1222222)  (1223)
%e A335449        (31)  (2112)  (2122)  (211222)  (132)  (2122222)  (1322)
%e A335449              (2211)  (2212)  (221122)  (213)  (2212222)  (2123)
%e A335449                      (2221)  (222112)  (231)  (2221222)  (2213)
%e A335449                              (222211)  (312)  (2222122)  (2231)
%e A335449                                        (321)  (2222212)  (3122)
%e A335449                                               (2222221)  (3212)
%e A335449                                                          (3221)
%t A335449 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A335449 Table[Length[Select[Permutations[primeMS[n]],!MatchQ[#,{___,x_,___,y_,___,x_,___}/;x<y]&]],{n,100}]
%Y A335449 The matching version is A335446.
%Y A335449 Patterns are counted by A000670.
%Y A335449 (1,2,1)-avoiding patterns are counted by A001710.
%Y A335449 Permutations of prime indices are counted by A008480.
%Y A335449 Unsorted prime signature is A124010. Sorted prime signature is A118914.
%Y A335449 (1,2,1) and (2,1,2)-avoiding permutations of prime indices are counted by A333175.
%Y A335449 STC-numbers of permutations of prime indices are A333221.
%Y A335449 (1,2,1) and (2,1,2)-avoiding permutations of prime indices are A335448.
%Y A335449 Patterns matched by standard compositions are counted by A335454.
%Y A335449 (1,2,1) or (2,1,2)-matching permutations of prime indices are A335460.
%Y A335449 (1,2,1) and (2,1,2)-matching permutations of prime indices are A335462.
%Y A335449 Dimensions of downsets of standard compositions are A335465.
%Y A335449 (1,2,1)-avoiding compositions are ranked by A335467.
%Y A335449 (1,2,1)-avoiding compositions are counted by A335471.
%Y A335449 Cf. A056239, A056986, A112798, A158005, A181796, A335452, A335463.
%K A335449 nonn
%O A335449 1,6
%A A335449 _Gus Wiseman_, Jun 14 2020