login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A038098 Number of primes < n^3. 5
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
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 range(1, 45)] # Zerinvary Lajos, Jun 06 2009
(PARI) vector(100, n, primepi(n^3)) \\ Altug Alkan, Oct 17 2015
CROSSREFS
Cf. A014085, A038107, A060199 (first differences).
Sequence in context: A008020 A244096 A008146 * A299274 A111384 A196039
KEYWORD
nonn
AUTHOR
Joe K. Crump (joecr(AT)carolina.rr.com)
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)