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Table read by antidiagonals: T(n,k) (n>=2) = number of factorizations of (n,k) into pairs (i,j) with i,j>1.
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%I #3 Mar 30 2012 17:37:15

%S 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,

%T 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,

%U 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

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

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

%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)-1)*(zeta(t)-1).

%e 1 1 1 1 1 ...

%e 1 1 1 1 1 ...

%e 1 1 2 1 2 ...

%e 1 1 1 1 1 ...

%e 1 1 2 1 3 ...

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

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

%K nonn,tabl

%O 2,13

%A _Christian G. Bower_, Jun 03 2005