A124829 Table of exponents of prime factorizations in A055932.

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, 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, 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

Offset: 1

Author

Franklin T. Adams-Watters, Nov 09 2006

Keywords

• nonn
• tabf

Comments

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

Examples

			From _Michael De Vlieger_, Feb 06 2020: (Start)
Table begins:
   n   A055932(n+1)  row n
   ---------------------
   1    2            1;
   2    4            2;
   3    6            1, 1;
   4    8            3;
   5   12            2, 1;
   6   16            4;
   7   18            1, 2;
   8   24            3, 1;
   9   30            1, 1, 1;
  10   32            5;
  11   36            2, 2;
  12   48            4, 1;
  13   54            1, 3;
  14   60            2, 1, 1;
  15   64            6;
  ...  (End)
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10382 (rows 1 <= n <= 2500).

Crossrefs

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

Programs

Mathematica

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

Formula

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