cp's OEIS Frontend

A335125 Number of anti-run permutations of a multiset whose multiplicities are the prime indices of n.

%I A335125 #9 Jan 08 2021 20:39:52
%S A335125 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 A335125 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 A335125 0,0,24,720,0,0,0,0,0,14,0,660,0,0,74,0,1,0,0
%N A335125 Number of anti-run permutations of a multiset whose multiplicities are the prime indices of n.
%C A335125 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 A335125 An anti-run is a sequence with no adjacent equal parts.
%e A335125 The a(n) permutations for n = 2, 4, 42, 8, 30, 18:
%e A335125   (1)  (12)  (1212131)  (123)  (121213)  (12123)
%e A335125        (21)  (1213121)  (132)  (121231)  (12132)
%e A335125              (1312121)  (213)  (121312)  (12312)
%e A335125                         (231)  (121321)  (12321)
%e A335125                         (312)  (123121)  (13212)
%e A335125                         (321)  (131212)  (21213)
%e A335125                                (132121)  (21231)
%e A335125                                (212131)  (21312)
%e A335125                                (213121)  (21321)
%e A335125                                (312121)  (23121)
%e A335125                                          (31212)
%e A335125                                          (32121)
%t A335125 nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A335125 Table[Length[Select[Permutations[nrmptn[n]],!MatchQ[#,{___,x_,x_,___}]&]],{n,100}]
%Y A335125 Positions of zeros are A335126.
%Y A335125 Positions of nonzeros are A335127.
%Y A335125 The version for the prime indices themselves is A335452.
%Y A335125 Anti-run compositions are A003242.
%Y A335125 Anti-runs are ranked by A333489.
%Y A335125 Separable partitions are ranked by A335433.
%Y A335125 Separable factorizations are A335434.
%Y A335125 Inseparable partitions are ranked by A335448.
%Y A335125 Patterns contiguously matched by compositions are A335457.
%Y A335125 Strict permutations of prime indices are A335489.
%Y A335125 Cf. A019472, A056239, A106351, A112798, A114938, A278990, A292884, A325535, A335407, A335463, A335516, A335838.
%K A335125 nonn
%O A335125 1,4
%A A335125 _Gus Wiseman_, Jul 01 2020