A343341 Number of integer partitions of n with no part divisible by all the others.

1, 0, 0, 0, 0, 1, 1, 4, 6, 11, 16, 28, 36, 58, 79, 111, 149, 209, 270, 368, 472, 618, 793, 1030, 1292, 1653, 2073, 2608, 3241, 4051, 4982, 6176, 7566, 9285, 11320, 13805, 16709, 20275, 24454, 29477, 35380, 42472, 50741, 60648, 72199, 85887, 101906, 120816

Offset

0,8

Comments

Alternative name: Number of integer partitions of n that are either empty, or have greatest part not divisible by all the others.

Links

Table of n, a(n) for n=0..47.

Example

The a(5) = 1 through a(10) = 16 partitions:
  (32)  (321)  (43)    (53)     (54)      (64)
               (52)    (332)    (72)      (73)
               (322)   (431)    (432)     (433)
               (3211)  (521)    (522)     (532)
                       (3221)   (531)     (541)
                       (32111)  (3222)    (721)
                                (3321)    (3322)
                                (4311)    (4321)
                                (5211)    (5221)
                                (32211)   (5311)
                                (321111)  (32221)
                                          (33211)
                                          (43111)
                                          (52111)
                                          (322111)
                                          (3211111)

Mathematica

Table[Length[Select[IntegerPartitions[n], #=={}||!And@@IntegerQ/@(Max@@#/#)&]], {n, 0, 30}]

Crossrefs

The complement is counted by A130689.

The dual version is A338470.

The Heinz numbers of these partitions are A343337.

The strict case is A343377.

A000009 counts strict partitions.

A000041 counts partitions.

A000070 counts partitions with a selected part.

A006128 counts partitions with a selected position.

A015723 counts strict partitions with a selected part.

Cf. A066186, A083710, A083711, A097986, A098965, A341450, A343342, A343345, A343346, A343381, A343382.

Sequence in context: A190499 A190564 A008369 * A343345 A343346 A296468

Adjacent sequences: A343338 A343339 A343340 * A343342 A343343 A343344

Keyword

nonn

Author

Gus Wiseman, Apr 15 2021

Status

approved