A379634 Irregular triangle read by rows in which row n lists the odd divisors of n ordered as the mirror of A261697.

1, 1, 3, 1, 1, 5, 1, 3, 1, 7, 1, 1, 3, 9, 1, 5, 1, 11, 1, 3, 1, 13, 1, 7, 1, 5, 3, 15, 1, 1, 17, 1, 9, 3, 1, 19, 1, 5, 1, 7, 3, 21, 1, 11, 1, 23, 1, 3, 1, 5, 25, 1, 13, 1, 9, 3, 27, 1, 7, 1, 29, 1, 5, 15, 3, 1, 31, 1, 1, 11, 3, 33, 1, 17, 1, 7, 5, 35, 1, 9, 3, 1, 37, 1, 19, 1, 13, 3, 39, 1, 5, 1, 41, 1, 7, 21, 3, 1, 43, 1, 11, 1

Offset: 1

Author

Omar E. Pol, Dec 31 2024

Keywords

• nonn
• tabf

Comments

Row n gives the last A001227(n) terms of the n-th row of A379630 and of A379631.

For a correspondence between the row n and the partitions of n into consecutive parts see A379630.

Examples

			Triangle begins:
   1;
   1;
   3,  1;
   1;
   5,  1;
   3,  1;
   7,  1;
   1;
   3,  9,  1;
   5,  1;
  11,  1;
   3,  1;
  13,  1;
   7,  1;
   5,  3, 15,  1;
   1;
  17,  1;
   9,  3,  1;
  19,  1;
   5,  1;
   7,  3, 21,  1;
  11,  1;
  23,  1;
   3,  1;
   5, 25,  1;
  13,  1;
   9,  3, 27,  1;
   7,  1;
  ...
Illustration of initial terms:
   Row    _
   1     |1|_
   2     |_ 1|_
   3     |3|  1|_
   4     | |_   1|_
   5     |_ 5|    1|_
   6     |3| |_     1|_
   7     | |  7|      1|_
   8     | |_  |_       1|_
   9     |_ 3|  9|        1|_
  10     |5| |   |_         1|_
  11     | | |_  11|          1|_
  12     | |  3|   |_           1|_
  13     | |_  |   13|            1|_
  14     |_ 7| |_    |_             1|_
  15     |5| |  3|   15|              1|_
  16     | | |   |     |_               1|_
  17     | | |_  |_    17|                1|_
  18     | |  9|  3|     |_                 1|_
  19     | |_  |   |     19|                  1|_
  20     |_ 5| |   |_      |_                   1|_
  21     |7| | |_   3|     21|                    1|_
  22     | | | 11|   |       |_                     1|_
  23     | | |   |   |_      23|                      1|_
  24     | | |_  |    3|       |_                       1|_
  25     | |  5| |_    |       25|                        1|_
  26     | |_  | 13|   |_        |_                          1|_
  27     |_ 9| |   |    3|       27|                           1|_
  28     |7| | |   |     |         |                             1|
  ...
The diagram is also the right part of the diagram of A379630 and of A379631.
The geometrical structure is the same as the diagram of A261350 which is the mirror of A237591.
		

Crossrefs

Mirror of A261697.

Right border gives A000012.

Row lengths give A001227.

Row sums give A000593.

Other versions are A182469, A261697, A261698.

Cf. A196020, A235791, A236104, A237048, A237591, A237593, A261350, A261699, A379630, A379631, A379632, A379633.