A124829 - OEIS

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

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OFFSET

1,2

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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)

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A355534 A296150 A079673 * A093394 A094363 A124832

Adjacent sequences: A124826 A124827 A124828 * A124830 A124831 A124832

KEYWORD

nonn,tabf

AUTHOR

Franklin T. Adams-Watters, Nov 09 2006

STATUS

approved