A336104 -id:A336104 - cp's OEIS frontend

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

Gus Wiseman, Sep 03 2020

nonn

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.

			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)

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.

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

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

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

cp's OEIS Frontend

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

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