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 A036380 #22 Mar 22 2025 04:42:58
%S A036380 0,1,1,2,3,2,4,3,4,6,5,9,10,11,17,15,26,31,39,53,68,90,125,159,216,
%T A036380 290,391,536,719,971,1329,1812,2477,3386,4626,6351,8729,11995,16459,
%U A036380 22669,31259,43049,59388,82024,113275,156558,216560,299566,414821,574654
%N A036380 Number of true prime powers whose binary order, ceiling(log_2(p^x)), is n.
%H A036380 Amiram Eldar, <a href="/A036380/b036380.txt">Table of n, a(n) for n = 1..150</a>
%F A036380 a(n) = A036386(n) - A036386(n-1) for n >= 2. - _Amiram Eldar_, Mar 22 2025
%e A036380 There are 5 prime powers between 2^10 + 1 = 1025 and 2^11 = 2048 (inclusive): 1331 = 11^3, 1369 = 37^2, 1681 = 41^2, 1849 = 43^2, and 2048 = 2^11, so a(11) = 5.
%t A036380 t=Table[Length[Union[Flatten[Table[Table[Prime[w]^s, {w, 1, PrimePi[2^(n/s)]}], {s, 2, g+1}]]] ], {n, 1, 42}]; Delete[t-RotateRight[t], 1]
%Y A036380 Cf. A029837, A036378-A036390.
%K A036380 nonn
%O A036380 1,4
%A A036380 _Labos Elemer_
%E A036380 More terms from _Sean A. Irvine_, Oct 29 2020