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%I #22 Aug 20 2021 14:46:00
%S 1,3,6,10,18,27,44,70,117,198,340,604,1078,1961,3590,6635,12370,23150,
%T 43579,82267,155921,296347,564688,1078555,2064589,3958999,7605134,
%U 14632960,28195586,54403835,105102701,203287169,393625231,762951922
%N Rank of 2^n when all prime powers (A246655) p^n, for n>=1, are jointly ranked.
%H Ray Chandler, <a href="/A182908/b182908.txt">Table of n, a(n) for n = 1..92</a> (using b-file file from A007053)
%F a(n) = A182908(n) = A024622(n) - 1 for n>=1.
%F a(n) = Sum_{i=1..n} pi(floor(2^(n/i))), where pi(n) = A000720(n). - _Ridouane Oudra_, Oct 26 2020
%e a(3)=6 because 2^3 has rank 6 in the sequence (2,3,4,5,7,8,9,...).
%t 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 f[n_] := Sum[ PrimePi[ Floor[2^(n/k)]], {k, n + 1}]; Array[f, 34] (* _Robert G. Wilson v_, Jul 08 2011 *)
%Y Cf. A000720, A024622, A246655.
%Y Row 1 of A182869. Complement of A182909.
%K nonn
%O 1,2
%A _Clark Kimberling_, Dec 13 2010
%E Minor edits by _Ray Chandler_, Aug 20 2021
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