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 A383963 #39 Jun 25 2025 00:35:00
%S A383963 2,3,3,4,4,5,4,5,6,6,7,5,5,7,8,8,9,6,6,9,10,6,10,11,7,7,11,12,12,13,8,
%T A383963 7,7,8,13,14,14,15,9,9,15,16,8,8,16,17,10,8,10,17,18,18,19,11,9,9,11,
%U A383963 19,20,20,21,12,9,9,12,21,22,10,10,22,23,13,13,23,24,24,25,14,11,10,10,11,14,25
%N A383963 Irregular triangle read by rows: T(n,k) is the sum of the k-th pair of conjugate divisors of n. If n is a square then the central term in the row n is equal to 2*sqrt(n), with n >= 1, 1 <= k <= A000005(n).
%C A383963 Row n is a palindromic composition of A074400(n) = 2*A000203(n).
%C A383963 Shares infinitely many rows with the virtual sequence 2*A237270.
%F A383963 T(n,k) = A027750(n,k) + A056538(n,k).
%e A383963 Triangle begins:
%e A383963 n | Row n
%e A383963 1 | 2;
%e A383963 2 | 3, 3;
%e A383963 3 | 4, 4;
%e A383963 4 | 5, 4, 5;
%e A383963 5 | 6, 6;
%e A383963 6 | 7, 5, 5, 7;
%e A383963 7 | 8, 8;
%e A383963 8 | 9, 6, 6, 9;
%e A383963 9 | 10, 6, 10;
%e A383963 10 | 11, 7, 7, 11;
%e A383963 11 | 12, 12;
%e A383963 12 | 13, 8, 7, 7, 8, 13;
%e A383963 13 | 14, 14;
%e A383963 14 | 15, 9, 9, 15;
%e A383963 15 | 16, 8, 8, 16;
%e A383963 16 | 17, 10, 8, 10, 17;
%e A383963 ...
%e A383963 For n = 8 the divisors of 8 are [1, 2, 4, 8] and the sums of the conjugate divisors are respectively [1 + 8 = 9], [2 + 4 = 6], [4 + 2 = 6], [8 + 1 = 9], so the 8th row is [9, 6, 6, 9].
%e A383963 For n = 9 the divisors of 9 are [1, 3, 9] and the sums of the conjugate divisors are respectively [1 + 9 = 10], [3 + 3 = 6], [9 + 1 = 10], so the 9th row is [10, 6, 10]. Since 9 is a square then the central term in the row is equal to 2*sqrt(9) = 2*3 = 6. Also in this case the 9th row is the same as the 9th row of the virtual sequence 2*A237270 because the 9th row of A237270 is [5, 3, 5].
%t A383963 row[n_] := Module[{d = Divisors[n]}, d + Reverse[d]]; Array[row, 24] // Flatten (* _Amiram Eldar_, Jun 18 2025 *)
%o A383963 (PARI) row(n) = my(d=divisors(n)); vector(#d, k, d[k]+n/d[k]); \\ _Michel Marcus_, Jun 18 2025
%Y A383963 Row lengths give A000005.
%Y A383963 Row sums give A074400 = 2*A000203.
%Y A383963 Column 1 gives A000027 except the 1, the same for the right border.
%Y A383963 Cf. A027750, A056538, A237270, A272025.
%K A383963 nonn,tabf
%O A383963 1,1
%A A383963 _Omar E. Pol_, Jun 17 2025