OFFSET
1,3
COMMENTS
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..11480 (rows 1..40 of the triangle, flattened)
EXAMPLE
Triangle begins:
[1];
[1, 2], [1];
[1, 0, 3], [1, 2], [2];
[1, 2, 0, 4], [1, 0, 3], [2, 4], [3];
[1, 0, 0, 0, 5], [1, 2, 0, 4], [2, 0, 6], [3, 6], [5];
[...
Row sums give A066186.
Written as an irregular tetrahedron the first five slices are:
--
1;
-----
1, 2,
1;
--------
1, 0, 3,
1, 2,
2;
-----------
1, 2, 0, 4,
1, 0, 3,
2, 4,
3;
--------------
1, 0, 0, 0, 5,
1, 2, 0, 4,
2, 0, 6,
3, 6,
5;
--------------
Row sums give A339106.
The following table formed by four zones shows the correspondence between divisor and parts (n = 1..5):
.
|---|---------|-----|-------|---------|-----------|-------------|
| n | | 1 | 2 | 3 | 4 | 5 |
|---|---------|-----|-------|---------|-----------|-------------|
| P | | | | | | |
| A | | | | | | |
| R | | | | | | |
| T | | | | | | 5 |
| I | | | | | | 3 2 |
| T | | | | | 4 | 4 1 |
| I | | | | | 2 2 | 2 2 1 |
| O | | | | 3 | 3 1 | 3 1 1 |
| N | | | 2 | 2 1 | 2 1 1 | 2 1 1 1 |
| S | | 1 | 1 1 | 1 1 1 | 1 1 1 1 | 1 1 1 1 1 |
|---|---------|-----|-------|---------|-----------|-------------|
.
|---|---------|-----|-------|---------|-----------|-------------|
| | A181187 | 1 | 3 1 | 6 2 1 | 12 5 2 1 | 20 8 4 2 1 |
| L | | | | |/| | |/|/| | |/|/|/| | |/|/|/|/| |
| I | A066633 | 1 | 2 1 | 4 1 1 | 7 3 1 1 | 12 4 2 1 1 |
| N | | * | * * | * * * | * * * * | * * * * * |
| K | A002260 | 1 | 1 2 | 1 2 3 | 1 2 3 4 | 1 2 3 4 5 |
| | | = | = = | = = = | = = = = | = = = = = |
| | A138785 | 1 | 2 2 | 4 2 3 | 7 6 3 4 | 12 8 6 4 5 |
|---|---------|-----|-------|---------|-----------|-------------|
.
|---|---------|-----|-------|---------|-----------|-------------|
| | A127093 | 1 | 1 2 | 1 0 3 | 1 2 0 4 | 1 0 0 0 5 |
| |---------|-----|-------|---------|-----------|-------------|
| | A127093 | | 1 | 1 2 | 1 0 3 | 1 2 0 4 |
| |---------|-----|-------|---------|-----------|-------------|
| D | A127093 | | | 1 | 1 2 | 1 0 3 |
| I | A127093 | | | 1 | 1 2 | 1 0 3 |
| V |---------|-----|-------|---------|-----------|-------------|
| I | A127093 | | | | 1 | 1 2 |
| S | A127093 | | | | 1 | 1 2 |
| O | A127093 | | | | 1 | 1 2 |
| R |---------|-----|-------|---------|-----------|-------------|
| S | A127093 | | | | | 1 |
| | A127093 | | | | | 1 |
| | A127093 | | | | | 1 |
| | A127093 | | | | | 1 |
| | A127093 | | | | | 1 |
|---|---------|-----|-------|---------|-----------|-------------|
.
|---|---------|-----|-------|---------|-----------|-------------|
| | A127093 | 1 | 1 2 | 1 0 3 | 1 2 0 4 | 1 0 0 0 5 |
| C | A127093 | | 1 | 1 2 | 1 0 3 | 1 2 0 4 |
| O | - | | | 2 | 2 4 | 2 0 6 |
| N | - | | | | 3 | 3 6 |
| D | - | | | | | 5 |
|---|---------|-----|-------|---------|-----------|-------------|
.
This lower zone of the table is a condensed version of the "divisors" zone.
MATHEMATICA
A127093row[n_]:=Table[Boole[Divisible[n, k]]k, {k, n}];
A340011row[n_]:=Flatten[Table[A127093row[n-m+1]PartitionsP[m-1], {m, n}]];
Array[A340011row, 10] (* Paolo Xausa, Sep 28 2023 *)
CROSSREFS
Row sums give A066186.
Nonzero terms give A340056.
Cf. A000070, A000041, A002260, A026792, A027750, A058399, A066633, A127093, A135010, A138121, A138785, A176206, A181187, A182703, A207031, A207383, A211992, A221529, A221530, A221531, A221649, A221650, A237593, A245095, A302246, A302247, A336811, A336812, A337209, A338156, A339106, A339258, A339278, A339304, A340031, A340032, A340035, A340061.
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Dec 26 2020
STATUS
approved