A182908 Rank of 2^n when all prime powers (A246655) p^n, for n>=1, are jointly ranked.

1, 3, 6, 10, 18, 27, 44, 70, 117, 198, 340, 604, 1078, 1961, 3590, 6635, 12370, 23150, 43579, 82267, 155921, 296347, 564688, 1078555, 2064589, 3958999, 7605134, 14632960, 28195586, 54403835, 105102701, 203287169, 393625231, 762951922

Offset

1,2

Links

Ray Chandler, Table of n, a(n) for n = 1..92 (using b-file file from A007053)

Formula

a(n) = A182908(n) = A024622(n) - 1 for n>=1.

a(n) = Sum_{i=1..n} pi(floor(2^(n/i))), where pi(n) = A000720(n). - Ridouane Oudra, Oct 26 2020

Example

a(3)=6 because 2^3 has rank 6 in the sequence (2,3,4,5,7,8,9,...).

Mathematica

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}]]
f[n_] := Sum[ PrimePi[ Floor[2^(n/k)]], {k, n + 1}]; Array[f, 34] (* Robert G. Wilson v, Jul 08 2011 *)

Crossrefs

Cf. A000720, A024622, A246655.

Row 1 of A182869. Complement of A182909.

Sequence in context: A291608 A182152 A170803 * A076251 A261631 A029864

Adjacent sequences: A182905 A182906 A182907 * A182909 A182910 A182911

Keyword

nonn

Author

Clark Kimberling, Dec 13 2010

Extensions

Minor edits by Ray Chandler, Aug 20 2021

Status

approved