OFFSET
1,2
COMMENTS
From Zhi-Wei Sun, Oct 17 2015: (Start)
Conjecture: (i) For any integer k > 2 the sequence pi(n^k)/n^k (n = 2,3,...) is strictly decreasing, where pi(x) denotes the number of primes not exceeding x.
(ii) All the numbers pi(n^2)/n^2 (n = 1,2,3,...) are pairwise distinct. Moreover, we have pi(n^2)/n^2 > pi((n+1)^2)/(n+1)^2 for all n > 15646.
(End)
LINKS
R. J. Mathar, Table of n, a(n) for n = 1..500
FORMULA
EXAMPLE
a(2)=4 because the only primes < 8 are 2,3,5 and 7.
PROG
(Sage) [prime_pi(n^3) for n in range(1, 45)] # Zerinvary Lajos, Jun 06 2009
(PARI) vector(100, n, primepi(n^3)) \\ Altug Alkan, Oct 17 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Joe K. Crump (joecr(AT)carolina.rr.com)
STATUS
approved