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%I #7 Jun 22 2020 01:53:41
%S 1,1,1,1,1,2,1,0,1,2,1,2,1,2,2,0,1,2,1,2,2,2,1,0,1,2,0,2,1,6,1,0,2,2,
%T 2,2,1,2,2,0,1,6,1,2,2,2,1,0,1,2,2,2,1,0,2,0,2,2,1,6,1,2,2,0,2,6,1,2,
%U 2,6,1,0,1,2,2,2,2,6,1,0,0,2,1,6,2,2,2
%N Number of permutations of the prime indices of n with all equal parts contiguous and none appearing more than twice.
%C 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.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%F a(n) = A001221(n)! if n is cubefree, otherwise 0.
%e The a(90) = 6 permutations are (1,2,2,3), (1,3,2,2), (2,2,1,3), (2,2,3,1), (3,1,2,2), (3,2,2,1).
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Table[Length[Select[Permutations[primeMS[n]],!MatchQ[#,{___,x_,__,x_,___}]&]],{n,100}]
%Y Separations are counted by A003242 and A335452 and ranked by A333489.
%Y Permutations of prime indices are counted by A008480.
%Y Unsorted prime signature is A124010. Sorted prime signature is A118914.
%Y Permutations of prime indices with equal parts contiguous are A333175.
%Y STC-numbers of permutations of prime indices are A333221.
%Y (1,2,1) and (2,1,2)-avoiding permutations of prime indices are A333175.
%Y Numbers whose prime indices are inseparable are A335448.
%Y (1,2,1) or (2,1,2)-matching permutations of prime indices are A335460.
%Y (1,2,1) and (2,1,2)-matching permutations of prime indices are A335462.
%Y Strict permutations of prime indices are counted by A335489.
%Y Cf. A056239, A056986, A112798, A181796, A335446, A335463.
%K nonn
%O 1,6
%A _Gus Wiseman_, Jun 21 2020
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