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 A323053 #7 Jan 04 2019 17:31:34
%S A323053 1,0,1,1,2,2,3,4,6,7,9,12,15,19,25,30,38,47,58,71,87,106,131,156,190,
%T A323053 228,275,328,394,468,556,661,784,923,1089,1283,1507,1766,2068,2416,
%U A323053 2821,3284,3822,4438,5148,5961,6898,7968,9195,10593,12198,14019,16102,18472
%N A323053 Number of integer partitions of n with no 1's such that no part is a power of any other (unequal) part.
%e A323053 The a(2) = 1 through a(11) = 12 integer partitions (A = 10, B = 11):
%e A323053 (2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
%e A323053 (22) (32) (33) (43) (44) (54) (55) (65)
%e A323053 (222) (52) (53) (63) (64) (74)
%e A323053 (322) (62) (72) (73) (83)
%e A323053 (332) (333) (433) (92)
%e A323053 (2222) (522) (532) (443)
%e A323053 (3222) (622) (533)
%e A323053 (3322) (632)
%e A323053 (22222) (722)
%e A323053 (3332)
%e A323053 (5222)
%e A323053 (32222)
%t A323053 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A323053 Table[Length[Select[IntegerPartitions[n],And[FreeQ[#,1],stableQ[#,IntegerQ[Log[#1,#2]]&]]&]],{n,30}]
%Y A323053 Cf. A001597, A002865, A007916, A052410, A101417, A102430, A108917, A305148, A305630, A305631, A321346, A323093.
%K A323053 nonn
%O A323053 0,5
%A A323053 _Gus Wiseman_, Jan 04 2019