cp's OEIS Frontend

A108461 Table read by antidiagonals: T(n,k) = number of factorizations of (n,k) into pairs (i,j) with i,j>=1, not both 1.

%I A108461 #9 Dec 08 2017 12:11:25
%S A108461 1,1,1,1,2,1,2,2,2,2,1,4,2,4,1,2,2,4,4,2,2,1,5,2,9,2,5,1,3,2,5,4,4,5,
%T A108461 2,3,2,7,2,11,2,11,2,7,2,2,4,7,4,5,5,4,7,4,2,1,5,4,16,2,15,2,16,4,5,1,
%U A108461 4,2,5,9,7,5,5,7,9,5,2,4,1,11,2,11,4,21,2,21,4,11,2,11,1,2,2,11,4,5,11,7
%N A108461 Table read by antidiagonals: T(n,k) = number of factorizations of (n,k) into pairs (i,j) with i,j>=1, not both 1.
%C A108461 The rule of building products is (a,b)*(x,y) = (a*x,b*y).
%C A108461 The number of divisors of (n,k) is A143235(n,k)-1, where the subtraction of 1 means that the unit (1,1) is not admitted here. - _R. J. Mathar_, Nov 30 2017
%H A108461 R. J. Mathar, <a href="/A108461/b108461.txt">Table of n, a(n) for n = 1..1711</a>, the first 59 diagonals.
%H A108461 R. J. Mathar, <a href="/A108461/a108461.txt">Java Source code of 2 files to generate the b-file</a>
%F A108461 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 A108461 1 1 1 2 1 ...
%e A108461 1 2 2 4 2 ...
%e A108461 1 2 2 4 2 ...
%e A108461 2 4 4 9 4 ...
%e A108461 1 2 2 4 2 ...
%e A108461 (6,2)=(6,1)*(1,2)=(3,2)*(2,1)=(3,1)*(2,2)=(1,2)*(6,1), so a(6,2)=5.
%Y A108461 Cf. A051707, A108455-A108470.
%Y A108461 Columns 1-3: A001055, A057567, A057567.
%Y A108461 Main diagonal: A108462.
%K A108461 nonn,tabl
%O A108461 1,5
%A A108461 _Christian G. Bower_, Jun 03 2005