A326852 Number of non-constant integer partitions of n whose length and maximum both divide n.

0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 16, 0, 1, 7, 11, 0, 30, 0, 40, 18, 1, 0, 201, 0, 1, 38, 124, 0, 426, 0, 211, 73, 1, 48, 1391, 0, 1, 131, 1741, 0, 1774, 0, 951, 2145, 1, 0, 8345, 0, 1853, 381, 2382, 0, 6718, 2761, 10633, 623, 1, 0, 68037

Offset

0,13

Comments

The Heinz numbers of these partitions are given by A326838.

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..180

Example

The a(6) = 1 through a(16) = 11 partitions (empty columns not shown):
  (321)  (4211)  (52111)  (633)     (7211111)  (53322)  (8332)
                          (642)                (53331)  (8422)
                          (651)                (54222)  (8431)
                          (4332)               (54321)  (8521)
                          (4422)               (54411)  (8611)
                          (4431)               (55221)  (42222211)
                          (6222)               (55311)  (43222111)
                          (6321)                        (43321111)
                          (6411)                        (44221111)
                          (322221)                      (44311111)
                          (332211)                      (82111111)
                          (333111)
                          (422211)
                          (432111)
                          (441111)
                          (621111)

Mathematica

Table[Length[Select[IntegerPartitions[n], !SameQ@@#&&Divisible[n, Length[#]]&&Divisible[n, Max[#]]&]], {n, 0, 30}]

Crossrefs

The possibly constant case is A326843.

The strict case is A326851.

Cf. A018818, A047993, A067538, A326837, A326838, A326842, A326849.

Sequence in context: A228574 A007791 A294699 * A070570 A347158 A347160

Adjacent sequences: A326849 A326850 A326851 * A326853 A326854 A326855

Keyword

nonn

Author

Gus Wiseman, Jul 26 2019

Status

approved