A108455 - OEIS

%I #18 Oct 03 2021 19:27:48

%S 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,

%T 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,

%U 1,3,1,3,1,4,3,3,1,4,0,1,1,3,1,5,1,7,2

%N 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).

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

%F 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).

%e Table begins

%e   1 0 0 0 0 ...

%e   1 1 1 1 1 ...

%e   1 1 1 1 1 ...

%e   2 2 2 3 2 ...

%e   1 1 1 1 1 ...

%e   ...

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

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

%K nonn,tabl

%O 1,10

%A _Christian G. Bower_, Jun 03 2005

%E Definition clarified and original interpretation restored by _Sean A. Irvine_, Oct 03 2021