This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335432 #13 Feb 03 2021 13:49:25
%S A335432 1,1,1,2,1,1,1,6,2,6,2,36,1,6,6,24,1,24,1,240,6,24,2,1800,6,6,6,720,6,
%T A335432 1800,1,120,24,6,24,282240,2,6,24,15120,2,5760,6,5040,720,24,6,
%U A335432 1451520,2,5040,120,5040,6,1800,720,40320,24,720,2,1117670400,1,6,1800,5040,6
%N A335432 Number of anti-run permutations of the prime indices of Mersenne numbers A000225(n) = 2^n - 1.
%C A335432 An anti-run is a sequence with no adjacent equal parts.
%C A335432 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 A335432 Andrew Howroyd, <a href="/A335432/b335432.txt">Table of n, a(n) for n = 1..200</a>
%F A335432 a(n) = A335452(A000225(n)).
%e A335432 The a(1) = 1 through a(10) = 6 permutations:
%e A335432 () (2) (4) (2,3) (11) (2,4,2) (31) (2,3,7) (21,4) (11,2,5)
%e A335432 (3,2) (2,7,3) (4,21) (11,5,2)
%e A335432 (3,2,7) (2,11,5)
%e A335432 (3,7,2) (2,5,11)
%e A335432 (7,2,3) (5,11,2)
%e A335432 (7,3,2) (5,2,11)
%t A335432 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A335432 Table[Length[Select[Permutations[primeMS[2^n-1]],!MatchQ[#,{___,x_,x_,___}]&]],{n,0,30}]
%o A335432 (PARI) \\ See A335452 for count.
%o A335432 a(n) = {count(factor(2^n-1)[,2])} \\ _Andrew Howroyd_, Feb 03 2021
%Y A335432 The version for factorial numbers is A335407.
%Y A335432 Anti-run compositions are A003242.
%Y A335432 Anti-run patterns are A005649.
%Y A335432 Permutations of prime indices are A008480.
%Y A335432 Anti-runs are ranked by A333489.
%Y A335432 Separable partitions are ranked by A335433.
%Y A335432 Inseparable partitions are ranked by A335448.
%Y A335432 Anti-run permutations of prime indices are A335452.
%Y A335432 Strict permutations of prime indices are A335489.
%Y A335432 Cf. A056239, A106351, A112798, A114938, A278990, A292884, A325535, A335125.
%Y A335432 Mersenne numbers: A000225, A046051, A046800, A046801, A049093, A059305, A159611, A325610, A325611, A325612, A325625.
%K A335432 nonn
%O A335432 1,4
%A A335432 _Gus Wiseman_, Jul 02 2020
%E A335432 Terms a(51) and beyond from _Andrew Howroyd_, Feb 03 2021