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 A340056 #39 Sep 03 2023 11:15:35
%S A340056 1,1,2,1,1,3,1,2,2,1,2,4,1,3,2,4,3,1,5,1,2,4,2,6,3,6,5,1,2,3,6,1,5,2,
%T A340056 4,8,3,9,5,10,7,1,7,1,2,3,6,2,10,3,6,12,5,15,7,14,11,1,2,4,8,1,7,2,4,
%U A340056 6,12,3,15,5,10,20,7,21,11,22,15,1,3,9,1,2,4,8,2,14,3,6,9,18,5
%N A340056 Irregular triangle read by rows T(n,k) in which row n lists n blocks, where the m-th block consists of the divisors of j multiplied by A000041(m-1), where j = n - m + 1 and 1 <= m <= n.
%C A340056 This triangle is a condensed version of the more irregular triangle A338156 which is the main sequence with further information about the correspondence divisor/part.
%H A340056 Paolo Xausa, <a href="/A340056/b340056.txt">Table of n, a(n) for n = 1..11528</a> (rows 1..75 of the triangle, flattened)
%e A340056 Triangle begins:
%e A340056 [1];
%e A340056 [1, 2], [1];
%e A340056 [1, 3], [1, 2], [2];
%e A340056 [1, 2, 4], [1, 3], [2, 4], [3];
%e A340056 [1, 5], [1, 2, 4], [2, 6], [3, 6], [5];
%e A340056 [...
%e A340056 The row sums of triangle give A066186.
%e A340056 Written as an irregular tetrahedron the first five slices are:
%e A340056 1;
%e A340056 -----
%e A340056 1, 2,
%e A340056 1;
%e A340056 -----
%e A340056 1, 3,
%e A340056 1, 2,
%e A340056 2;
%e A340056 --------
%e A340056 1, 2, 4,
%e A340056 1, 3,
%e A340056 2, 4,
%e A340056 3;
%e A340056 --------
%e A340056 1, 5,
%e A340056 1, 2, 4,
%e A340056 2, 6,
%e A340056 3, 6,
%e A340056 5;
%e A340056 --------
%e A340056 The row sums of tetrahedron give A339106.
%e A340056 The slices of the tetrahedron appear in the following table formed by four zones shows the correspondence between divisor and parts (n = 1..5):
%e A340056 .
%e A340056 |---|---------|-----|-------|---------|-----------|-------------|
%e A340056 | n | | 1 | 2 | 3 | 4 | 5 |
%e A340056 |---|---------|-----|-------|---------|-----------|-------------|
%e A340056 | P | | | | | | |
%e A340056 | A | | | | | | |
%e A340056 | R | | | | | | |
%e A340056 | T | | | | | | 5 |
%e A340056 | I | | | | | | 3 2 |
%e A340056 | T | | | | | 4 | 4 1 |
%e A340056 | I | | | | | 2 2 | 2 2 1 |
%e A340056 | O | | | | 3 | 3 1 | 3 1 1 |
%e A340056 | N | | | 2 | 2 1 | 2 1 1 | 2 1 1 1 |
%e A340056 | S | | 1 | 1 1 | 1 1 1 | 1 1 1 1 | 1 1 1 1 1 |
%e A340056 |---|---------|-----|-------|---------|-----------|-------------|
%e A340056 .
%e A340056 |---|---------|-----|-------|---------|-----------|-------------|
%e A340056 | | A181187 | 1 | 3 1 | 6 2 1 | 12 5 2 1 | 20 8 4 2 1 |
%e A340056 | L | | | | |/| | |/|/| | |/|/|/| | |/|/|/|/| |
%e A340056 | I | A066633 | 1 | 2 1 | 4 1 1 | 7 3 1 1 | 12 4 2 1 1 |
%e A340056 | N | | * | * * | * * * | * * * * | * * * * * |
%e A340056 | K | A002260 | 1 | 1 2 | 1 2 3 | 1 2 3 4 | 1 2 3 4 5 |
%e A340056 | | | = | = = | = = = | = = = = | = = = = = |
%e A340056 | | A138785 | 1 | 2 2 | 4 2 3 | 7 6 3 4 | 12 8 6 4 5 |
%e A340056 |---|---------|-----|-------|---------|-----------|-------------|
%e A340056 .
%e A340056 |---|---------|-----|-------|---------|-----------|-------------|
%e A340056 | | A027750 | 1 | 1 2 | 1 3 | 1 2 4 | 1 5 |
%e A340056 | |---------|-----|-------|---------|-----------|-------------|
%e A340056 | | A027750 | | 1 | 1 2 | 1 3 | 1 2 4 |
%e A340056 | |---------|-----|-------|---------|-----------|-------------|
%e A340056 | D | A027750 | | | 1 | 1 2 | 1 3 |
%e A340056 | I | A027750 | | | 1 | 1 2 | 1 3 |
%e A340056 | V |---------|-----|-------|---------|-----------|-------------|
%e A340056 | I | A027750 | | | | 1 | 1 2 |
%e A340056 | S | A027750 | | | | 1 | 1 2 |
%e A340056 | O | A027750 | | | | 1 | 1 2 |
%e A340056 | R |---------|-----|-------|---------|-----------|-------------|
%e A340056 | S | A027750 | | | | | 1 |
%e A340056 | | A027750 | | | | | 1 |
%e A340056 | | A027750 | | | | | 1 |
%e A340056 | | A027750 | | | | | 1 |
%e A340056 | | A027750 | | | | | 1 |
%e A340056 |---|---------|-----|-------|---------|-----------|-------------|
%e A340056 .
%e A340056 |---|---------|-----|-------|---------|-----------|-------------|
%e A340056 | | A027750 | 1 | 1 2 | 1 3 | 1 2 4 | 1 5 |
%e A340056 | C | A027750 | | 1 | 1 2 | 1 3 | 1 2 4 |
%e A340056 | O | - | | | 2 | 2 4 | 2 6 |
%e A340056 | N | - | | | | 3 | 3 6 |
%e A340056 | D | - | | | | | 5 |
%e A340056 |---|---------|-----|-------|---------|-----------|-------------|
%e A340056 .
%e A340056 The lower zone is a condensed version of the "divisors" zone.
%t A340056 A340056row[n_]:=Flatten[Table[Divisors[n-m]PartitionsP[m],{m,0,n-1}]];Array[A340056row,10] (* _Paolo Xausa_, Sep 01 2023 *)
%Y A340056 Nonzero terms of A340011.
%Y A340056 Row sums give A066186.
%Y A340056 Cf. A000070, A000041, A002260, A026792, A027750, A058399, A066633, A127093, A135010, A138121, A138785, A176206, A181187, A182703, A207031, A207383, A211992, A221529, A221530, A221531, A245095, A221649, A221650, A237593, A302246, A302247, A336811, A336812, A337209, A338156, A339106, A339258, A339278, A339304, A340061.
%K A340056 nonn,tabf
%O A340056 1,3
%A A340056 _Omar E. Pol_, Dec 27 2020