OFFSET
1,3
LINKS
Ray Chandler, Table of n, a(n) for n = 1..125 (first 112 terms from Hiroaki Yamanouchi)
FORMULA
a(n) = Sum_{j=2..n+1} pi(floor(2^(n/j))). The summation starts with squares(j=2); for arbitrary range (=y), the y^(1/j) argument has to be used.
EXAMPLE
The 9 prime powers not exceeding 64 are 4, 8, 9, 16, 25, 27, 32, 49, 64.
n = 25, a(25) = 900, pi(5792) + pi(322) + pi(76) + pi(32) + pi(17) + pi(11) + pi(8) + pi(6) + pi(5) + pi(4) + pi(4) + pi(3) + pi(3) + pi(3) + pi(2) + pi(2) + pi(2) + pi(2) + pi(2) + pi(2) + pi(2) + pi(2) + pi(2) + pi(2) + pi(1) = 760 + 66 + 21 + 11 + 7 + 5 + 4 + 3 + 3 + 2 + 2 + 2 + 2 + 2 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 0.
MATHEMATICA
f[n_] := Length@ Union@ Flatten@ Table[ Prime[j]^k, {k, 2, n + 1}, {j, PrimePi[2^(n/k)]}]; Array[f, 46] (* Robert G. Wilson v, Jul 08 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Labos Elemer, May 07 2001
Terms a(47) and beyond from Hiroaki Yamanouchi, Nov 15 2016
STATUS
approved