A336105 Number of permutations of the prime indices of 2^n - 1.

1, 1, 1, 2, 1, 3, 1, 6, 2, 6, 2, 60, 1, 6, 6, 24, 1, 120, 1, 360, 12, 24, 2, 2520, 6, 6, 6, 720, 6, 2520, 1, 120, 24, 6, 24, 604800, 2, 6, 24, 20160, 2, 10080, 6, 5040, 720, 24, 6, 1814400, 2, 5040, 120, 5040, 6, 15120, 720, 40320, 24, 720, 2

Offset

1,4

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..59.

Formula

a(n) = A008480(2^n - 1).

a(n) = A336104(n) + A335432(n).

Example

The a(n) permutations for n = 2, 4, 6, 8, 21:
  (2)  (2,3)  (2,2,4)  (2,3,7)  (31,4,4,68)
       (3,2)  (2,4,2)  (2,7,3)  (31,4,68,4)
              (4,2,2)  (3,2,7)  (31,68,4,4)
                       (3,7,2)  (4,31,4,68)
                       (7,2,3)  (4,31,68,4)
                       (7,3,2)  (4,4,31,68)
                                (4,4,68,31)
                                (4,68,31,4)
                                (4,68,4,31)
                                (68,31,4,4)
                                (68,4,31,4)
                                (68,4,4,31)

Mathematica

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

Crossrefs

A008480 is not restricted to predecessors of powers of 2.

A325617 is the version for factorial numbers.

A335489 counts strict permutations of prime indices.

Cf. A056239, A112798, A335432, A336104.

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

Sequence in context: A277130 A082588 A006241 * A282601 A363273 A034869

Adjacent sequences: A336102 A336103 A336104 * A336106 A336107 A336108

Keyword

nonn

Author

Gus Wiseman, Sep 03 2020

Status

approved