A300351 Triangle whose n-th row lists in order all Heinz numbers of integer partitions of n into odd parts.

1, 2, 4, 5, 8, 10, 16, 11, 20, 32, 22, 25, 40, 64, 17, 44, 50, 80, 128, 34, 55, 88, 100, 160, 256, 23, 68, 110, 125, 176, 200, 320, 512, 46, 85, 121, 136, 220, 250, 352, 400, 640, 1024, 31, 92, 170, 242, 272, 275, 440, 500, 704, 800, 1280, 2048, 62, 115, 184

Offset: 1

Author

Gus Wiseman, Mar 03 2018

Keywords

• nonn
• tabf

Comments

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Examples

			Triangle of partitions into odd parts begins:
                   0
                  (1)
                  (11)
                (3) (111)
               (31) (1111)
            (5) (311) (11111)
        (51) (33) (3111) (111111)
    (7) (511) (331) (31111) (1111111)
(71) (53) (5111) (3311) (311111) (11111111)
		

Crossrefs

Cf. A000009, A031368, A056239, A066208, A078408, A215366, A246867, A299759, A299757, A300063, A300272.

Programs

Mathematica

Table[Sort[Times@@Prime/@#&/@Select[IntegerPartitions[n],And@@OddQ/@#&]],{n,0,12}]