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A038098 Number of primes < n^3. 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 (list; graph; refs; listen; history; text; internal format)
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

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

EXAMPLE

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

PROG

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

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

CROSSREFS

Sequence in context: A008020 A244096 A008146 * A111384 A196039 A238091

Adjacent sequences:  A038095 A038096 A038097 * A038099 A038100 A038101

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified April 25 00:32 EDT 2017. Contains 285346 sequences.