A323094 Number of strict integer partitions of n where no part is 2^k times any other part, for any k > 0.

1, 1, 1, 1, 2, 2, 2, 4, 4, 4, 5, 7, 8, 10, 12, 12, 15, 17, 20, 24, 27, 33, 35, 41, 48, 54, 61, 69, 79, 87, 101, 113, 128, 144, 159, 181, 201, 225, 251, 281, 311, 347, 388, 428, 477, 525, 579, 643, 712, 788, 868, 954, 1051, 1155, 1272, 1398, 1534, 1682, 1840, 2016

Offset: 0

Author

Gus Wiseman, Jan 04 2019

Keywords

• nonn

Examples

			The a(1) = 1 through a(12) = 8 strict integer partitions (A = 10, B = 11, C = 12):
  (1)  (2)  (3)  (4)   (5)   (6)   (7)   (8)   (9)    (A)    (B)    (C)
                 (31)  (32)  (51)  (43)  (53)  (54)   (64)   (65)   (75)
                                   (52)  (62)  (72)   (73)   (74)   (93)
                                   (61)  (71)  (531)  (91)   (83)   (A2)
                                                      (532)  (92)   (B1)
                                                             (A1)   (543)
                                                             (731)  (651)
                                                                    (732)
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A018819, A087897, A120641, A276431, A303362, A323054, A323092, A323093.

Programs

Mathematica

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