A038098 Number of primes < n^3.

0, 4, 9, 18, 30, 47, 68, 97, 129, 168, 217, 269, 327, 400, 476, 564, 656, 765, 882, 1007, 1147, 1298, 1457, 1633, 1821, 2020, 2227, 2460, 2707, 2961, 3228, 3512, 3817, 4137, 4483, 4821, 5194, 5579, 5995, 6413, 6850, 7308, 7789, 8293

Offset: 1

Author

Joe K. Crump (joecr(AT)carolina.rr.com)

Keywords

• nonn

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)

Examples

			a(2)=4 because the only primes < 8 are 2,3,5 and 7.
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A014085, A038107, A060199 (first differences).

Programs

PARI

vector(100, n, primepi(n^3)) \\ Altug Alkan, Oct 17 2015

Sage

[prime_pi(n^3) for n in range(1, 45)] # Zerinvary Lajos, Jun 06 2009

Formula

a(n) = A000720(A000578(n)). - Michel Marcus, Sep 02 2013