VOOZH about

URL: https://oeis.org/A182908

⇱ A182908 - OEIS

login
A182908
Rank of 2^n when all prime powers (A246655) p^n, for n>=1, are jointly ranked.
8
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, 1480223716, 2874422303
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
a(n) = A025528(2^n). - Pontus von Brömssen, Sep 27 2024
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 *)
PROG
(Python)
from sympy import primepi, integer_nthroot
def A182908(n):
x = 1<<n
return int(sum(primepi(integer_nthroot(x, k)[0]) for k in range(1, n+1))) # Chai Wah Wu, Nov 05 2024
CROSSREFS
Row 1 of A182869. Complement of A182909.
Sequence in context: A291608 A182152 A170803 * A076251 A261631 A029864
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 13 2010
EXTENSIONS
Minor edits by Ray Chandler, Aug 20 2021
STATUS
approved