A115628 Factorization of n! into primorials.

1, 0, 1, 2, 1, 2, 0, 1, 2, 1, 1, 2, 1, 0, 1, 5, 1, 0, 1, 3, 3, 0, 1, 4, 2, 1, 1, 4, 2, 1, 0, 1, 5, 3, 1, 0, 1, 5, 3, 1, 0, 0, 1, 6, 3, 0, 1, 0, 1, 5, 3, 1, 1, 0, 1, 9, 3, 1, 1, 0, 1, 9, 3, 1, 1, 0, 0, 1, 8, 5, 1, 1, 0, 0, 1, 8, 5, 1, 1, 0, 0, 0, 1, 10, 4, 2, 1, 0, 0, 0, 1, 9, 5, 1, 2, 0, 0, 0, 1, 10, 5, 1, 1, 1

Offset: 2

Author

Franklin T. Adams-Watters, Jan 26 2006

Keywords

• nonn
• tabf

Comments

Factorial of n has a unique representation as a product of primorials: n! = 2#^T(n,1)*3#^T(n,2)*...*P_{Pi(n)}#^T(n,Pi(n)).

Examples

			Rows start: 1; 0,1; 2,1; 2,0,1; 2,1,1; 2,1,0,1; 5,1,0,1; 3,3,0,1.
		

Crossrefs

Cf. A115627, A000142, A002110. Row lengths are A000720.

Formula

T(n, k) = A115727(n, k)-A115727(n, k+1).