A323093 Number of integer partitions of n where no part is 2^k times any other part, for any k > 0.

1, 1, 2, 2, 4, 4, 6, 9, 12, 13, 18, 23, 29, 37, 49, 55, 71, 84, 104, 126, 153, 185, 221, 261, 317, 375, 446, 523, 623, 721, 854, 994, 1168, 1357, 1579, 1833, 2126, 2455, 2843, 3270, 3766, 4320, 4980, 5687, 6521, 7444, 8498, 9684, 11039, 12540, 14262

Offset

0,3

Links

Table of n, a(n) for n=0..50.

Example

The a(1) = 1 through a(8) = 12 integer partitions:
  (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)
       (11)  (111)  (22)    (32)     (33)      (43)       (44)
                    (31)    (311)    (51)      (52)       (53)
                    (1111)  (11111)  (222)     (61)       (62)
                                     (3111)    (322)      (71)
                                     (111111)  (331)      (332)
                                               (511)      (611)
                                               (31111)    (2222)
                                               (1111111)  (3311)
                                                          (5111)
                                                          (311111)
                                                          (11111111)

Mathematica

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

Crossrefs

Cf. A018819, A101417, A120641, A276431, A305148, A323092, A323094.

Sequence in context: A276065 A325253 A143483 * A264788 A192326 A131733

Adjacent sequences: A323090 A323091 A323092 * A323094 A323095 A323096

Keyword

nonn

Author

Gus Wiseman, Jan 04 2019

Status

approved