|
%I #11 Sep 11 2020 11:46:15
%S 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,
%T 6,2520,1,120,24,6,24,604800,2,6,24,20160,2,10080,6,5040,720,24,6,
%U 1814400,2,5040,120,5040,6,15120,720,40320,24,720,2
%N Number of permutations of the prime indices of 2^n - 1.
%C 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.
%F a(n) = A008480(2^n - 1).
%F a(n) = A336104(n) + A335432(n).
%e The a(n) permutations for n = 2, 4, 6, 8, 21:
%e (2) (2,3) (2,2,4) (2,3,7) (31,4,4,68)
%e (3,2) (2,4,2) (2,7,3) (31,4,68,4)
%e (4,2,2) (3,2,7) (31,68,4,4)
%e (3,7,2) (4,31,4,68)
%e (7,2,3) (4,31,68,4)
%e (7,3,2) (4,4,31,68)
%e (4,4,68,31)
%e (4,68,31,4)
%e (4,68,4,31)
%e (68,31,4,4)
%e (68,4,31,4)
%e (68,4,4,31)
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Table[Length[Permutations[primeMS[2^n-1]]],{n,30}]
%Y A008480 is not restricted to predecessors of powers of 2.
%Y A325617 is the version for factorial numbers.
%Y A335489 counts strict permutations of prime indices.
%Y Cf. A056239, A112798, A335432, A336104.
%Y The numbers 2^n - 1: A000225, A046051, A046800, A046801, A049093, A325610, A325611, A325612, A325625.
%K nonn
%O 1,4
%A _Gus Wiseman_, Sep 03 2020
|
