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 A350634 #12 Feb 04 2024 18:46:36
%S A350634 1,2,3,4,4,6,5,8,9,6,10,12,7,12,15,16,8,14,18,20,9,16,21,24,25,10,18,
%T A350634 24,28,30,11,20,27,32,35,36,12,22,30,36,40,42,13,24,33,40,45,48,49,14,
%U A350634 26,36,44,50,54,56,15,28,39,48,55,60,63,64,16,30,42,52,60,66,70,72
%N A350634 Products of the parts s,t in each partition of k (= 2,3,...) into two parts, ordered by increasing k and then by increasing values of s*t (see example).
%C A350634 If b > 0 and c > 0 are the integer coefficients of a monic quadratic x^2 + b*x + c, it has integer roots if its discriminant d^2 = b^2 - 4c is a perfect square. This sequence is the values of c for increasing b sorted by b then c. The first pair of (b, c) = (2, 1) and has d = 0. The n-th pair of (b, c) = (A027434(n),a(n)) and has d = A082375(n-1). - _Frank M Jackson_, Jan 22 2024
%F A350634 a(n) = A122197(n) * A199474(n).
%F A350634 a(n) = A339399(2n-1) * A339399(2n).
%F A350634 a(n) = ((A027434(n))^2 - (A082375(n))^2)/4. - _Frank M Jackson_, Jan 22 2024
%e A350634 ---------------------------------------------------------------------------
%e A350634 The products of the parts start: 1*1, 1*2, 1*3, 2*2, 1*4, 2*3, etc., which are precisely the values of a(n): 1, 2, 3, 4, 4, 6, ...
%e A350634 [1,9]
%e A350634 [1,7] [1,8] [2,8]
%e A350634 [1,5] [1,6] [2,6] [2,7] [3,7]
%e A350634 [1,3] [1,4] [2,4] [2,5] [3,5] [3,6] [4,6]
%e A350634 [1,1] [1,2] [2,2] [2,3] [3,3] [3,4] [4,4] [4,5] [5,5]
%e A350634 k 2 3 4 5 6 7 8 9 10
%e A350634 ---------------------------------------------------------------------------
%t A350634 Times@@@Flatten[Table[IntegerPartitions[k, {2}], {k, 2, 100}], 1] (* _Frank M Jackson_, Jan 22 2024 *)
%t A350634 lst={}; Do[If[IntegerQ[d=Sqrt[b^2-4c]], AppendTo[lst, c]], {b, 1, 100}, {c, 1, b^2/4}]; lst (* _Frank M Jackson_, Jan 22 2024 *)
%Y A350634 Cf. A027434, A082375, A122197, A199474, A339399.
%K A350634 nonn
%O A350634 1,2
%A A350634 _Wesley Ivan Hurt_, Jan 09 2022