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A336104 Number of permutations of the prime indices of A000225(n) = 2^n - 1 with at least one non-singleton run. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 19:02 EST 2021. Contains 349424 sequences. (Running on oeis4.)