cp's OEIS Frontend

A336104 Number of permutations of the prime indices of A000225(n) = 2^n - 1 with at least one non-singleton run.

%I A336104 #12 Sep 08 2020 02:19:52
%S A336104 0,0,0,0,0,2,0,0,0,0,0,24,0,0,0,0,0,96,0,120,6,0,0,720,0,0,0,0,0,720,
%T A336104 0,0,0,0,0,322560,0,0,0,5040,0,4320,0,0,0,0,0,362880,0,0
%N A336104 Number of permutations of the prime indices of A000225(n) = 2^n - 1 with at least one non-singleton run.
%C A336104 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.
%F A336104 a(n) = A336107(2^n - 1).
%F A336104 a(n) = A336105(n) - A335432(n).
%e A336104 The a(21) = 6 permutations of {4, 4, 31, 68}:
%e A336104   (4,4,31,68)
%e A336104   (4,4,68,31)
%e A336104   (31,4,4,68)
%e A336104   (31,68,4,4)
%e A336104   (68,4,4,31)
%e A336104   (68,31,4,4)
%t A336104 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A336104 Table[Length[Select[Permutations[primeMS[2^n-1]],MatchQ[#,{___,x_,x_,___}]&]],{n,30}]
%Y A336104 A335432 is the anti-run version.
%Y A336104 A335459 is the version for factorial numbers.
%Y A336104 A336105 counts all permutations of this multiset.
%Y A336104 A336107 is not restricted to predecessors of powers of 2.
%Y A336104 A003242 counts anti-run compositions.
%Y A336104 A005649 counts anti-run patterns.
%Y A336104 A008480 counts permutations of prime indices.
%Y A336104 A325534 counts separable partitions, ranked by A335433.
%Y A336104 A325535 counts inseparable partitions, ranked by A335448.
%Y A336104 A333489 ranks anti-run compositions.
%Y A336104 A335433 lists numbers whose prime indices have an anti-run permutation.
%Y A336104 A335448 lists numbers whose prime indices have no anti-run permutation.
%Y A336104 A335452 counts anti-run permutations of prime indices.
%Y A336104 A335489 counts strict permutations of prime indices.
%Y A336104 Cf. A056239, A106351, A112798, A114938, A292884, A336102.
%Y A336104 The numbers 2^n - 1: A000225, A001265, A001348, A046051, A046800, A046801, A049093, A325610, A325611, A325612, A325625.
%K A336104 nonn,more
%O A336104 1,6
%A A336104 _Gus Wiseman_, Sep 03 2020