A124829 - OEIS

%I #6 Feb 06 2020 20:54:29

%S 1,2,1,1,3,2,1,4,1,2,3,1,1,1,1,5,2,2,4,1,1,3,2,1,1,6,3,2,1,2,1,5,1,2,

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

%U 2,2,4,3,2,1,7,1,2,1,1,1,4,3,1,2,2,5,1,1,1,5,9,2,3,1,6,2,3,1,2,1,2,1,1,3,4

%N Table of exponents of prime factorizations in A055932.

%C This is an enumeration of all compositions. This sequence contains all finite sequences of positive integers.

%H Michael De Vlieger, <a href="/A124829/b124829.txt">Table of n, a(n) for n = 1..10382</a> (rows 1 <= n <= 2500).

%F A055932(n) = Product_k Prime(k)^T(n,k).

%e From _Michael De Vlieger_, Feb 06 2020: (Start)

%e Table begins:

%e    n   A055932(n+1)  row n

%e    ---------------------

%e    1    2            1;

%e    2    4            2;

%e    3    6            1, 1;

%e    4    8            3;

%e    5   12            2, 1;

%e    6   16            4;

%e    7   18            1, 2;

%e    8   24            3, 1;

%e    9   30            1, 1, 1;

%e   10   32            5;

%e   11   36            2, 2;

%e   12   48            4, 1;

%e   13   54            1, 3;

%e   14   60            2, 1, 1;

%e   15   64            6;

%e   ...  (End)

%t Map[FactorInteger[#][[All, -1]] &, Select[Range[10^3], Last[#] == Length[#] &@ PrimePi@ FactorInteger[#][[All, 1]] &]] // Flatten (* _Michael De Vlieger_, Feb 06 2020 *)

%Y Cf. A055932, A124830 (row lengths), A124831 (row sums), A124832, A066099.

%K nonn,tabf

%O 1,2

%A _Franklin T. Adams-Watters_, Nov 09 2006