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

2,4

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)).

Links

Table of n, a(n) for n=2..105.

Formula

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

Example

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.

Sequence in context: A321104 A127442 A357524 * A114002 A114004 A306518

Adjacent sequences: A115625 A115626 A115627 * A115629 A115630 A115631

Keyword

nonn,tabf

Author

Franklin T. Adams-Watters, Jan 26 2006

Status

approved