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A335489 Number of strict permutations of the prime indices of n.

%I A335489 #10 Jun 30 2020 09:55:55
%S A335489 1,1,1,0,1,2,1,0,0,2,1,0,1,2,2,0,1,0,1,0,2,2,1,0,0,2,0,0,1,6,1,0,2,2,
%T A335489 2,0,1,2,2,0,1,6,1,0,0,2,1,0,0,0,2,0,1,0,2,0,2,2,1,0,1,2,0,0,2,6,1,0,
%U A335489 2,6,1,0,1,2,0,0,2,6,1,0,0,2,1,0,2,2,2
%N A335489 Number of strict permutations of the prime indices of n.
%C A335489 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 A335489 Also the number of (1,1)-avoiding permutations of the prime indices of n.
%H A335489 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335489 Gus Wiseman, <a href="https://oeis.org/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%F A335489 If n is squarefree, a(n) = A001221(n)!; otherwise a(n) = 0.
%F A335489 a(n != 4) = A281188(n); a(4) = 0.
%t A335489 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A335489 Table[Length[Select[Permutations[primeMS[n]],!MatchQ[#,{___,x_,___,x_,___}]&]],{n,100}]
%Y A335489 Positions of first appearances are A002110 with 2 replaced by 4.
%Y A335489 Permutations of prime indices are counted by A008480.
%Y A335489 The contiguous version is A335451.
%Y A335489 Anti-run permutations of prime indices are counted by A335452.
%Y A335489 (1,1,1)-avoiding permutations of prime indices are counted by A335511.
%Y A335489 Cf. A056239, A056986, A106356, A112798, A238279, A281188, A333221, A335456, A335460, A335462, A335465.
%K A335489 nonn
%O A335489 1,6
%A A335489 _Gus Wiseman_, Jun 19 2020