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A335510 Number of (1,1,1)-matching permutations of the prime indices of n.

%I A335510 #9 Jun 30 2020 01:55:07
%S A335510 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,4,0,0,1,0,0,0,0,1,0,0,
%T A335510 0,0,0,0,0,4,0,0,0,0,0,0,0,5,0,0,0,0,0,4,0,4,0,0,0,0,0,0,0,1,0,0,0,0,
%U A335510 0,0,0,10,0,0,0,0,0,0,0,5,1,0,0,0,0,0,0
%N A335510 Number of (1,1,1)-matching permutations of the prime indices of n.
%C A335510 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 A335510 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 A335510 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335510 Gus Wiseman, <a href="https://oeis.org/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%F A335510 If n is cubefree, a(n) = 0; otherwise a(n) = A008480(n).
%t A335510 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A335510 Table[Length[Select[Permutations[primeMS[n]],MatchQ[#,{___,x_,___,x_,___,x_,___}]&]],{n,0,100}]
%Y A335510 Patterns matching this pattern are counted by A335508.
%Y A335510 These compositions are counted by A335455.
%Y A335510 The (1,1)-matching version is A335487.
%Y A335510 The complement A335511 is the avoiding version.
%Y A335510 These permutations are ranked by A335512.
%Y A335510 Permutations of prime indices are counted by A008480.
%Y A335510 Patterns are counted by A000670 and ranked by A333217.
%Y A335510 Anti-run permutations of prime indices are counted by A335452.
%Y A335510 Cf. A056239, A056986, A112798, A238279, A281188, A333221, A333755, A335456, A335460, A335462, A335463.
%K A335510 nonn
%O A335510 1,24
%A A335510 _Gus Wiseman_, Jun 19 2020