A323054 Number of strict integer partitions of n with no 1's such that no part is a power of any other part.

1, 0, 1, 1, 1, 2, 1, 3, 3, 4, 4, 6, 6, 8, 9, 12, 13, 16, 19, 21, 25, 30, 36, 40, 47, 53, 63, 71, 83, 94, 107, 121, 140, 159, 180, 204, 233, 260, 296, 334, 377, 421, 474, 532, 598, 668, 750, 835, 933, 1038, 1163, 1292, 1435, 1597, 1771, 1966, 2180, 2421, 2673

Offset

0,6

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..350

Example

The a(2) = 1 through a(13) = 8 strict integer partitions (A = 10, B = 11, C = 12, D = 13):
  (2)  (3)  (4)  (5)   (6)  (7)   (8)   (9)   (A)    (B)    (C)    (D)
                 (32)       (43)  (53)  (54)  (64)   (65)   (75)   (76)
                            (52)  (62)  (63)  (73)   (74)   (84)   (85)
                                        (72)  (532)  (83)   (A2)   (94)
                                                     (92)   (543)  (A3)
                                                     (632)  (732)  (B2)
                                                                   (643)
                                                                   (652)

Mathematica

stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[Select[IntegerPartitions[n], And[FreeQ[#, 1], UnsameQ@@#, stableQ[#, IntegerQ[Log[#1, #2]]&]]&]], {n, 30}]

Crossrefs

Cf. A001597, A007916, A025147, A052410, A078374, A087897, A120641, A275972, A303362, A323053, A323087, A323088.

Sequence in context: A282611 A187498 A029137 * A339396 A027157 A112194

Adjacent sequences: A323051 A323052 A323053 * A323055 A323056 A323057

Keyword

nonn

Author

Gus Wiseman, Jan 04 2019

Status

approved