OFFSET
1,4
COMMENTS
EXAMPLE
Triangle begins:
[1];
[1],[1, 2];
[1],[1, 2],[1, 3],[1];
[1],[1, 2],[1, 3],[1],[1, 2, 4],[1, 2],[1];
[1],[1, 2],[1, 3],[1],[1, 2, 4],[1, 2],[1],[1, 5],[1, 3],[1, 2],[1],[1];
...
Below the table shows the correspondence divisor/part.
|---|-----------------|-----|-------|---------|-----------|-------------|
| 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 |
|---|-----------------|-----|-------|---------|-----------|-------------|
.
. |-------|
. |Section|
|---|-------|---------|-----|-------|---------|-----------|-------------|
| | 1 | A000012 | 1 | 1 | 1 | 1 | 1 |
| |-------|---------|-----|-------|---------|-----------|-------------|
| | 2 | A000034 | | 1 2 | 1 2 | 1 2 | 1 2 |
| |-------|---------|-----|-------|---------|-----------|-------------|
| D | 3 | A010684 | | | 1 3 | 1 3 | 1 3 |
| I | | A000012 | | | 1 | 1 | 1 |
| V |-------|---------|-----|-------|---------|-----------|-------------|
| I | 4 | A069705 | | | | 1 2 4 | 1 2 4 |
| S | | A000034 | | | | 1 2 | 1 2 |
| O | | A000012 | | | | 1 | 1 |
| R |-------|---------|-----|-------|---------|-----------|-------------|
| S | 5 | A010686 | | | | | 1 5 |
| | | A010684 | | | | | 1 3 |
| | | A000034 | | | | | 1 2 |
| | | A000012 | | | | | 1 |
| | | A000012 | | | | | 1 |
|---|-------|---------|-----|-------|---------|-----------|-------------|
.
In the above table both the zone of partitions and the "Link" zone are the same zones as in the table of the example section of A338156, but here in the lower zone the divisors are ordered in accordance with the sections of the set of partitions of n.
The number of rows in the j-th section of the lower zone is equal to A000041(j-1).
The divisors of the j-th section are also the parts of the j-th section of the set of partitions of n.
CROSSREFS
Another version of A338156.
Row n has length A006128(n).
The sum of row n is A066186(n).
The product of row n is A007870(n).
Row n lists the first n rows of A336812.
The number of parts k in row n is A066633(n,k).
The sum of all parts k in row n is A138785(n,k).
The number of parts >= k in row n is A181187(n,k).
The sum of all parts >= k in row n is A206561(n,k).
The number of parts <= k in row n is A210947(n,k).
The sum of all parts <= k in row n is A210948(n,k).
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Jul 31 2021
STATUS
approved