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 A182908 #31 Nov 05 2024 20:39:55
%S A182908 1,3,6,10,18,27,44,70,117,198,340,604,1078,1961,3590,6635,12370,23150,
%T A182908 43579,82267,155921,296347,564688,1078555,2064589,3958999,7605134,
%U A182908 14632960,28195586,54403835,105102701,203287169,393625231,762951922,1480223716,2874422303
%N A182908 Rank of 2^n when all prime powers (A246655) p^n, for n>=1, are jointly ranked.
%H A182908 Ray Chandler, <a href="/A182908/b182908.txt">Table of n, a(n) for n = 1..92</a> (using b-file file from A007053)
%F A182908 a(n) = A182908(n) = A024622(n) - 1 for n>=1.
%F A182908 a(n) = Sum_{i=1..n} pi(floor(2^(n/i))), where pi(n) = A000720(n). - _Ridouane Oudra_, Oct 26 2020
%F A182908 a(n) = A025528(2^n). - _Pontus von Brömssen_, Sep 27 2024
%e A182908 a(3)=6 because 2^3 has rank 6 in the sequence (2,3,4,5,7,8,9,...).
%t A182908 T[i_,j_]:=Sum[Floor[j*Log[Prime[i]]/Log[Prime[h]]],{h,1,PrimePi[Prime[i]^j]}]; Flatten[Table[T[i,j],{i,1,1},{j,1,22}]]
%t A182908 f[n_] := Sum[ PrimePi[ Floor[2^(n/k)]], {k, n + 1}]; Array[f, 34] (* _Robert G. Wilson v_, Jul 08 2011 *)
%o A182908 (Python)
%o A182908 from sympy import primepi, integer_nthroot
%o A182908 def A182908(n):
%o A182908 x = 1<<n
%o A182908 return int(sum(primepi(integer_nthroot(x, k)[0]) for k in range(1, n+1))) # _Chai Wah Wu_, Nov 05 2024
%Y A182908 Cf. A000720, A024622, A025528, A246655.
%Y A182908 Row 1 of A182869. Complement of A182909.
%K A182908 nonn
%O A182908 1,2
%A A182908 _Clark Kimberling_, Dec 13 2010
%E A182908 Minor edits by _Ray Chandler_, Aug 20 2021