A136568 Irregular triangle read by rows: row n contains the distinct values (in numerical order) making up the nonzero exponents in the prime factorization of n. (Row 1 = (0).).

0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 3, 1, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 4, 2, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 6, 1, 1, 1, 1, 2, 1, 1

Offset: 1

Author

Leroy Quet, Jan 07 2008

Keywords

• nonn
• tabf

Comments

Row n, for n>=2, contains A071625(n) terms.

Examples

			4200 = 2^3 * 3^1 * 5^2 * 7^1. The exponents of the prime factorization are therefore 3,1,2,1. Therefore row 4200 is (1,2,3).
Table begins:
  0;
  1;
  1;
  2;
  1;
  1;
  1;
  3;
  2;
  1;
  1;
  1, 2;
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index to sequences related to prime signature.

Crossrefs

Cf. A071625, A136565.

Programs

Mathematica

Join[{0},Flatten[Rest[Table[Union[Transpose[FactorInteger[n]][[2]]],{n,100}]]]] (* Harvey P. Dale, Mar 19 2013 *)

PARI

row(n) = if(n == 1, [0], Set(factor(n)[,2])); \\ Amiram Eldar, Aug 04 2024

Extensions

More terms from Harvey P. Dale, Mar 19 2013