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 A059529 #10 Jul 09 2025 10:54:33
%S A059529 1,1,2,5,9,16,32,68,135,256,512,1059,2110,4096,8192,16745,33425,65536,
%T A059529 131072,266254,531924,1048576,2097152,4244214,8482454,16777216,
%U A059529 33554432,67741466,135417620,268435456,536870912,1082015434,2163280087,4294967296,8589934592
%N A059529 For 1 < x, each c(i) is "multiply" (*) or "divide" (/); a(n) is number of choices for c(0),...,c(n-1) so that 1 c(0) x^1 c(1) x^2,.., c(n-1) x^n is an integer.
%C A059529 From _Gus Wiseman_, Jul 04 2019: (Start)
%C A059529 Also the number of subsets of {1..n} whose sum is less than or equal to the sum of their complement. For example, the a(0) = 1 through a(5) = 16 subsets are:
%C A059529 {} {} {} {} {} {}
%C A059529 {1} {1} {1} {1}
%C A059529 {2} {2} {2}
%C A059529 {3} {3} {3}
%C A059529 {1,2} {4} {4}
%C A059529 {1,2} {5}
%C A059529 {1,3} {1,2}
%C A059529 {1,4} {1,3}
%C A059529 {2,3} {1,4}
%C A059529 {1,5}
%C A059529 {2,3}
%C A059529 {2,4}
%C A059529 {2,5}
%C A059529 {3,4}
%C A059529 {1,2,3}
%C A059529 {1,2,4}
%C A059529 (End)
%H A059529 Alois P. Heinz, <a href="/A059529/b059529.txt">Table of n, a(n) for n = 0..700</a>
%F A059529 a(0)=1; for 0<n, a(n) = A058377(n)+2^(n-1).
%e A059529 x = 3: for n = 2 there are 2 possibilities: 1*3*9=27 and 1/3*9=3. For n = 4 there are 9 possibilities: 1*3*9*27*81 1/3*9*27*81 1*3/9*27*81 1/3/9*27*81 1*3*9/27*81 1*3*9*27/81 1/3*9/27*81 1/3*9*27/81 1*3/9/27*81
%t A059529 Table[Length[Select[Subsets[Range[n]],Plus@@Complement[Range[n],#]>=Plus@@#&]],{n,0,10}] (* _Gus Wiseman_, Jul 04 2019 *)
%Y A059529 Cf. A058524, A058377.
%Y A059529 Cf. A053632, A063865, A326173, A326174, A326175.
%K A059529 nonn
%O A059529 0,3
%A A059529 _Naohiro Nomoto_, Feb 16 2001
%E A059529 More terms from _Alois P. Heinz_, Jun 13 2019