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 A328368 #17 Nov 04 2019 09:24:09
%S A328368 1,2,3,2,4,2,5,4,6,4,3,7,6,3,8,6,3,9,8,6,10,8,6,4,11,10,6,4,12,10,9,4,
%T A328368 13,12,9,4,14,12,9,8,15,14,12,8,5,16,14,12,8,5,17,16,12,8,5,18,16,15,
%U A328368 12,5,19,18,15,12,5,20,18,15,12,10,21,20,18,12,10,6,22,20,18,16,10,6,23,22,18,16,10,6
%N A328368 Irregular triangle read by rows: T(n,k) is the total number of parts in all partitions of all positive integers <= n into k consecutive parts.
%C A328368 Column k lists k times every nonzero multiple of k in nondecreasing order.
%C A328368 Column k lists the partial sums of the k-th column of triangle A285914.
%e A328368 Triangle begins:
%e A328368 1;
%e A328368 2;
%e A328368 3, 2;
%e A328368 4, 2;
%e A328368 5, 4;
%e A328368 6, 4, 3;
%e A328368 7, 6, 3;
%e A328368 8, 6, 3;
%e A328368 9, 8, 6;
%e A328368 10, 8, 6, 4;
%e A328368 11, 10, 6, 4;
%e A328368 12, 10, 9, 4;
%e A328368 13, 12, 9, 4;
%e A328368 14, 12, 9, 8;
%e A328368 15, 14, 12, 8, 5;
%e A328368 16, 14, 12, 8, 5;
%e A328368 17, 16, 12, 8, 5;
%e A328368 18, 16, 15, 12, 5;
%e A328368 19, 18, 15, 12, 5;
%e A328368 20, 18, 15, 12, 10;
%e A328368 21, 20, 18, 12, 10, 6;
%e A328368 22, 20, 18, 16, 10, 6;
%e A328368 23, 22, 18, 16, 10, 6;
%e A328368 24, 22, 21, 16, 10, 6;
%e A328368 25, 24, 21, 16, 15, 6;
%e A328368 26, 24, 21, 20, 15, 6;
%e A328368 27, 26, 24, 20, 15, 12;
%e A328368 28, 26, 24, 20, 15, 12, 7;
%e A328368 ...
%o A328368 (PARI) tt(n, k) = k*(if (k % 2, (n % k) == 0, ((n - k/2) % k) == 0)); \\ A285891
%o A328368 t(n, k) = sum(j=k*(k+1)/2, n, tt(j, k));
%o A328368 tabf(nn) = {for (n=1, nn, for (k=1, floor((sqrt(1+8*n)-1)/2), print1(t(n, k), ", "); ); print(); ); } \\ _Michel Marcus_, Nov 04 2019
%Y A328368 Row sums give A285899.
%Y A328368 Row n has length A003056(n).
%Y A328368 Column 1 gives A000027.
%Y A328368 Column k starts with k in the row A000217(k).
%Y A328368 Cf. A052928, A196020, A204217, A211343, A235791, A236104, A235791, A237048, A237591, A237593, A245579, A262612, A285900, A285914, A285891, A286000, A286001, A286013, A299765, A328361, A328365, A328371.
%K A328368 nonn,tabf
%O A328368 1,2
%A A328368 _Omar E. Pol_, Nov 02 2019