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

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, 0, 0, 0, 0, 0, 322560, 0, 0, 0, 5040, 0, 4320, 0, 0, 0, 0, 0, 362880, 0, 0

Offset

1,6

Comments

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.

Links

Table of n, a(n) for n=1..50.

Formula

a(n) = A336107(2^n - 1).

a(n) = A336105(n) - A335432(n).

Example

The a(21) = 6 permutations of {4, 4, 31, 68}:
  (4,4,31,68)
  (4,4,68,31)
  (31,4,4,68)
  (31,68,4,4)
  (68,4,4,31)
  (68,31,4,4)

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[Select[Permutations[primeMS[2^n-1]], MatchQ[#, {___, x_, x_, ___}]&]], {n, 30}]

Crossrefs

A335432 is the anti-run version.

A335459 is the version for factorial numbers.

A336105 counts all permutations of this multiset.

A336107 is not restricted to predecessors of powers of 2.

A003242 counts anti-run compositions.

A005649 counts anti-run patterns.

A008480 counts permutations of prime indices.

A325534 counts separable partitions, ranked by A335433.

A325535 counts inseparable partitions, ranked by A335448.

A333489 ranks anti-run compositions.

A335433 lists numbers whose prime indices have an anti-run permutation.

A335448 lists numbers whose prime indices have no anti-run permutation.

A335452 counts anti-run permutations of prime indices.

A335489 counts strict permutations of prime indices.

Cf. A056239, A106351, A112798, A114938, A292884, A336102.

The numbers 2^n - 1: A000225, A001265, A001348, A046051, A046800, A046801, A049093, A325610, A325611, A325612, A325625.

Sequence in context: A123298 A189877 A189868 * A110981 A019261 A019222

Adjacent sequences: A336101 A336102 A336103 * A336105 A336106 A336107

Keyword

nonn,more

Author

Gus Wiseman, Sep 03 2020

Status

approved