A108465 Table read by antidiagonals: T(n,k) (n>=2) = number of factorizations of (n,k) into pairs (i,j) with i,j>1.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 3, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 4, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1

Offset: 2

Author

Christian G. Bower, Jun 03 2005

Keywords

• nonn
• tabl

Comments

(a,b)*(x,y)=(a*x,b*y).

Examples

			1 1 1 1 1 ...
1 1 1 1 1 ...
1 1 2 1 2 ...
1 1 1 1 1 ...
1 1 2 1 3 ...
(8,6)=(4,3)*(2,2)=(4,2)*(2,3), so a(8,6)=3.
		

Crossrefs

Cf. A108461. Columns 4, 6: A038548 (n>1), A032741. Main diagonal: A108466.

Formula

Dirichlet g.f.: A(s, t) = exp(B(s, t)/1 + B(2*s, 2*t)/2 + B(3*s, 3*t)/3 + ...) where B(s, t) = (zeta(s)-1)*(zeta(t)-1).