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 A036539 #29 Aug 16 2024 16:42:07
%S A036539 1,1,4,5,11,22,44,89,178,351,702,1413,2817,5634,11273,22542,45077,
%T A036539 90150,180322,360621,721233,1442482,2884968,5769917,11539863,23079674,
%U A036539 46159310,92318616,184637146,369274400,738548882,1477097703,2954195153,5908390134,11816780283
%N A036539 a(n) is the number of numbers k with 2^(n-1) < k <= 2^n having a number of divisors that is a power of 2.
%F A036539 a(n) ~ c * 2^(n-1), where c = 0.687827... (A327839). - _Amiram Eldar_, Aug 16 2024
%e A036539 a(5) = 11: The following 11 numbers have numbers of divisors that are powers of 2: 17, 19, 21, 22, 23, 24, 26, 27, 29, 30 and 31 with 2, 2, 4, 4, 2, 8, 4, 4, 2, 8 and 2 divisors, respectively.
%t A036539 f[n_] := Boole[n == 2^IntegerExponent[n, 2]]; a[n_] := Sum[f[DivisorSigma[0, k]], {k, 2^(n - 1) + 1, 2^n}]; Array[a, 20] (* _Amiram Eldar_, Aug 16 2024 *)
%o A036539 (PARI) a(n)=sum(k=2^(n-1)+1,2^n, my(d=numdiv(k)); (d/(1<<valuation(d,2)))==1 ); \\ _Joerg Arndt_, Feb 27 2017
%Y A036539 Cf. A036537, A037992, A327839.
%K A036539 nonn
%O A036539 1,3
%A A036539 _Labos Elemer_
%E A036539 Name clarified and more terms from _Joerg Arndt_, Feb 27 2017
%E A036539 a(25)-a(28) from _Jon E. Schoenfield_, Jul 31 2018
%E A036539 a(29)-a(35) from _Jon E. Schoenfield_, Aug 04 2018