A323094 - OEIS

%I #11 Dec 30 2020 03:34:51

%S 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,

%T 69,79,87,101,113,128,144,159,181,201,225,251,281,311,347,388,428,477,

%U 525,579,643,712,788,868,954,1051,1155,1272,1398,1534,1682,1840,2016

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

%H Fausto A. C. Cariboni, <a href="/A323094/b323094.txt">Table of n, a(n) for n = 0..400</a>

%e The a(1) = 1 through a(12) = 8 strict integer partitions (A = 10, B = 11, C = 12):

%e   (1)  (2)  (3)  (4)   (5)   (6)   (7)   (8)   (9)    (A)    (B)    (C)

%e                  (31)  (32)  (51)  (43)  (53)  (54)   (64)   (65)   (75)

%e                                    (52)  (62)  (72)   (73)   (74)   (93)

%e                                    (61)  (71)  (531)  (91)   (83)   (A2)

%e                                                       (532)  (92)   (B1)

%e                                                              (A1)   (543)

%e                                                              (731)  (651)

%e                                                                     (732)

%t stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];

%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&stableQ[#,IntegerQ[Log[2,#1/#2]]&]&]],{n,30}]

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

%K nonn

%O 0,5

%A _Gus Wiseman_, Jan 04 2019