A114575 - OEIS

%I #4 Jul 21 2013 13:48:27

%S 1,1,2,2,2,2,2,3,3,3,4,3,2,4,2,4,4,1,5,2,3,2,4,2,3,3,3,4,3,3,2,5,5,3,

%T 7,4,3,3,4,5,2,5,4,3,6,5,3,4,4,1,4,5,5,6,4,5,6,3,4,2,4,5,7,9,3,6,7,8,

%U 5,3,5,7,5,5,7,3,5,6,6,6

%N Number of distinct prime factors of floor(e^n).

%e floor(e^3) = floor(20.08553) = 20. 20 has two distinct prime factors (2 and 5), therefore a(3) = 2.

%t Table[Length[FactorInteger[Floor[E^n]]], {n, 1, 80}]

%t PrimeNu[Floor[E^Range[80]]] (* _Harvey P. Dale_, Jul 21 2013 *)

%Y Cf. A001113 [decimal expansion of e].

%K nonn

%O 0,3

%A _Stefan Steinerberger_, Feb 17 2006