This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A323093 #9 Jan 08 2019 16:23:28
%S A323093 1,1,2,2,4,4,6,9,12,13,18,23,29,37,49,55,71,84,104,126,153,185,221,
%T A323093 261,317,375,446,523,623,721,854,994,1168,1357,1579,1833,2126,2455,
%U A323093 2843,3270,3766,4320,4980,5687,6521,7444,8498,9684,11039,12540,14262
%N A323093 Number of integer partitions of n where no part is 2^k times any other part, for any k > 0.
%e A323093 The a(1) = 1 through a(8) = 12 integer partitions:
%e A323093 (1) (2) (3) (4) (5) (6) (7) (8)
%e A323093 (11) (111) (22) (32) (33) (43) (44)
%e A323093 (31) (311) (51) (52) (53)
%e A323093 (1111) (11111) (222) (61) (62)
%e A323093 (3111) (322) (71)
%e A323093 (111111) (331) (332)
%e A323093 (511) (611)
%e A323093 (31111) (2222)
%e A323093 (1111111) (3311)
%e A323093 (5111)
%e A323093 (311111)
%e A323093 (11111111)
%t A323093 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A323093 Table[Length[Select[IntegerPartitions[n],stableQ[#,IntegerQ[Log[2,#1/#2]]&]&]],{n,30}]
%Y A323093 Cf. A018819, A101417, A120641, A276431, A305148, A323092, A323094.
%K A323093 nonn
%O A323093 0,3
%A A323093 _Gus Wiseman_, Jan 04 2019