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%I #9 Jan 08 2021 20:39:52
%S 1,1,0,2,0,1,0,6,2,0,0,6,0,0,1,24,0,12,0,2,0,0,0,36,2,0,30,0,0,10,0,
%T 120,0,0,1,84,0,0,0,24,0,3,0,0,38,0,0,240,2,18,0,0,0,246,0,6,0,0,0,96,
%U 0,0,24,720,0,0,0,0,0,14,0,660,0,0,74,0,1,0,0
%N Number of anti-run permutations of a multiset whose multiplicities are the prime indices of n.
%C A multiset whose multiplicities are the prime indices of n (such as row n of A305936) is not the same as the multiset of prime indices of n. For example, the prime indices of 12 are {1,1,2}, while a multiset whose multiplicities are {1,1,2} is {1,1,2,3}.
%C An anti-run is a sequence with no adjacent equal parts.
%e The a(n) permutations for n = 2, 4, 42, 8, 30, 18:
%e (1) (12) (1212131) (123) (121213) (12123)
%e (21) (1213121) (132) (121231) (12132)
%e (1312121) (213) (121312) (12312)
%e (231) (121321) (12321)
%e (312) (123121) (13212)
%e (321) (131212) (21213)
%e (132121) (21231)
%e (212131) (21312)
%e (213121) (21321)
%e (312121) (23121)
%e (31212)
%e (32121)
%t nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t Table[Length[Select[Permutations[nrmptn[n]],!MatchQ[#,{___,x_,x_,___}]&]],{n,100}]
%Y Positions of zeros are A335126.
%Y Positions of nonzeros are A335127.
%Y The version for the prime indices themselves is A335452.
%Y Anti-run compositions are A003242.
%Y Anti-runs are ranked by A333489.
%Y Separable partitions are ranked by A335433.
%Y Separable factorizations are A335434.
%Y Inseparable partitions are ranked by A335448.
%Y Patterns contiguously matched by compositions are A335457.
%Y Strict permutations of prime indices are A335489.
%Y Cf. A019472, A056239, A106351, A112798, A114938, A278990, A292884, A325535, A335407, A335463, A335516, A335838.
%K nonn
%O 1,4
%A _Gus Wiseman_, Jul 01 2020
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