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 A379635 #21 Jan 15 2025 22:44:30
%S A379635 1,3,3,4,9,4,7,12,12,7,6,21,16,21,6,12,18,28,28,18,12,8,36,24,49,24,
%T A379635 36,8,15,24,48,42,42,48,24,15,13,45,32,84,36,84,32,45,13,18,39,60,56,
%U A379635 72,72,56,60,39,18,12,54,52,105,48,144,48,105,52,54,12,28,36,72,91,90,96,96,90,91,72,36,28
%N A379635 Triangle read by rows: T(n,k) = A000203(k)*A000203(n-k+1), n >= 1, k >= 1.
%H A379635 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%e A379635 Triangle begins:
%e A379635 1;
%e A379635 3, 3;
%e A379635 4, 9, 4;
%e A379635 7, 12, 12, 7;
%e A379635 6, 21, 16, 21, 6;
%e A379635 12, 18, 28, 28, 18, 12;
%e A379635 8, 36, 24, 49, 24, 36, 8;
%e A379635 15, 24, 48, 42, 42, 48, 24, 15;
%e A379635 13, 45, 32, 84, 36, 84, 32, 45, 13;
%e A379635 18, 39, 60, 56, 72, 72, 56, 60, 39, 18;
%e A379635 12, 54, 52, 105, 48, 144, 48, 105, 52, 54, 12;
%e A379635 28, 36, 72, 91, 90, 96, 96, 90, 91, 72, 36, 28;
%e A379635 14, 84, 48, 126, 78, 180, 64, 180, 78, 126, 48, 84, 14;
%e A379635 ...
%e A379635 For n = 10 the calculation of the row 10 is as follows:
%e A379635 k A000203 T(10,k)
%e A379635 1 1 * 18 = 18
%e A379635 2 3 * 13 = 39
%e A379635 3 4 * 15 = 60
%e A379635 4 7 * 8 = 56
%e A379635 5 6 * 12 = 72
%e A379635 6 12 * 6 = 72
%e A379635 7 8 * 7 = 56
%e A379635 8 15 * 4 = 60
%e A379635 9 13 * 3 = 39
%e A379635 10 18 * 1 = 18
%e A379635 A000203
%e A379635 .
%t A379635 T[n_,k_]:=DivisorSigma[1,k]*DivisorSigma[1,n-k+1];Table[T[n,k],{n,12},{k,n }]//Flatten (* _James C. McMahon_, Jan 15 2025 *)
%o A379635 (PARI) T(n, k)=sigma(k)*sigma(n-k+1)
%Y A379635 Column 1 and leading diagonal give A000203.
%Y A379635 Middle diagonal gives A072861.
%Y A379635 Row sums give A000385.
%Y A379635 Cf. A221529.
%K A379635 nonn,tabl
%O A379635 1,2
%A A379635 _Omar E. Pol_, Jan 14 2025