A108455 Table read by antidiagonals: T(n,k) = number of factorizations of (n,k) into any number of pairs (i,j) with i > 0, j > 0 (and if i=1 then j=1).

1, 0, 1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 0, 1, 1, 2, 1, 2, 0, 1, 1, 3, 1, 3, 1, 0, 1, 1, 2, 1, 3, 1, 3, 0, 1, 1, 3, 1, 4, 1, 4, 2, 0, 1, 1, 2, 1, 3, 1, 4, 2, 2, 0, 1, 1, 3, 1, 5, 1, 6, 2, 3, 1, 0, 1, 1, 3, 1, 3, 1, 4, 3, 3, 1, 4, 0, 1, 1, 3, 1, 5, 1, 7, 2

Offset: 1

Author

Christian G. Bower, Jun 03 2005

Keywords

• nonn
• tabl

Comments

(a,b)*(x,y) = (a*x,b*y); unit is (1,1).

Examples

			Table begins
  1 0 0 0 0 ...
  1 1 1 1 1 ...
  1 1 1 1 1 ...
  2 2 2 3 2 ...
  1 1 1 1 1 ...
  ...
(6,4) = (3,4)*(2,1) = (3,1)*(2,4) = (3,2)*(2,2), so a(6,4)=4.
		

Crossrefs

Cf. A108461, A051707 (main diagonal), A348157. Column 1: A001055.

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)*(zeta(t)-1).

Extensions

Definition clarified and original interpretation restored by Sean A. Irvine, Oct 03 2021