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

1,2

Comments

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

Links

Table of n, a(n) for n=1..58.

Example

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)

Mathematica

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

Crossrefs

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

Sequence in context: A050539 A277101 A039895 * A105425 A199799 A032937

Adjacent sequences: A300348 A300349 A300350 * A300352 A300353 A300354

Keyword

nonn,tabf

Author

Gus Wiseman, Mar 03 2018

Status

approved