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.
f[a_,b_]:=(a*b)/(a+b); a=42;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]],AppendTo[lst,n]],{n,9!}];lst
Select[Range[2000], Divisible[42 #, 42 + #] &] (* Harvey P. Dale, May 09 2012 *)
f[a_,b_]:=(a*b)/(a+b); a=48;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]], AppendTo[lst,n]],{n,9!}];lst
Select[Range[2300],IntegerQ[(48#)/(48+#)]&] (* Harvey P. Dale, Dec 18 2018 *)
f[a_,b_]:=(a*b)/(a+b); a=60;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]], AppendTo[lst,n]],{n,9!}];lst
The triangle begins: 1 2 1 2 3 4 6 2 3 4 6 12 2 3 4 5 6 8 12 20 4 5 6 10 30 2 3 4 5 6 7 8 9 10 12 15 18 24 42 6 7 8 14 56 ...
for n from 1 to 10 do for m from 1 to n*(n+1) do if(n=m or m*n mod (m-n) = 0)then printf("%d, ",m): fi: od: od:
Row 6 is (2,3,4,5) because row 6 of irregular array A127730 is (3,6,12,30); and (6*3)/(6+3) = 2, (6*6)/(6+6) = 3, (6*12)/(6+12) = 4 and (6*30)/(6+30) = 5.
f[n_] := Select[Table[n*m/(n + m), {m, n^2}], IntegerQ];Table[f[n], {n, 2, 26}] // Flatten (* Ray Chandler, Feb 13 2007 *)
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