This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A348157 #4 Oct 03 2021 19:28:03
%S A348157 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 A348157 1,2,0,1,1,3,1,4,1,3,2,0,1,1,2,1,3,1,3,2,2,0,1,1,3,1,5,1,4,2,3,1,0,1,
%U A348157 1,3,1,3,1,3,3,3,1,3,0,1,1,3,1,5,1,5,2,4,1,5,1,0,1,1,2,1,4,1,3,3,3,1,5,1,2
%N A348157 Table read by antidiagonals: T(n,k) = number of factorizations of (n,k) into one or two pairs (i,j) with i > 0, j > 0 (and if i=1 then j=1).
%C A348157 (a,b)*(x,y) = (a*x,b*y); unit is (1,1).
%F A348157 For n > 1, T(n,m) = ceiling((tau(n)-2)*tau(m)/2) + 1, where tau(n) = A000005(n). - _Franklin T. Adams-Watters_, Jun 23 2010.
%e A348157 Table begins
%e A348157 1 0 0 0 0 ...
%e A348157 1 1 1 1 1 ...
%e A348157 1 1 1 1 1 ...
%e A348157 2 2 2 3 2 ...
%e A348157 1 1 1 1 1 ...
%e A348157 ...
%e A348157 (6,4) = (3,4)*(2,1) = (3,1)*(2,4) = (3,2)*(2,2), so a(6,4)=4.
%t A348157 rows = 14; t[n_, m_] := Ceiling[(DivisorSigma[0, n] - 2)*DivisorSigma[0, m]/2]+1; t[1, 1] = 1; t[1, _] = 0; ft = Flatten[ Table[ t[n-m+1, m], {n, 1, rows}, {m, n, 1, -1}]] (* _Jean-François Alcover_, Nov 18 2011, after _Franklin T. Adams-Watters_ *)
%Y A348157 Cf. A108455 (any number of pairs), A108461. Column 1: A001055.
%K A348157 nonn,tabl
%O A348157 1,10
%A A348157 _Sean A. Irvine_, Oct 03 2021