

A065855


Number of composites <= n.


44



0, 0, 0, 1, 1, 2, 2, 3, 4, 5, 5, 6, 6, 7, 8, 9, 9, 10, 10, 11, 12, 13, 13, 14, 15, 16, 17, 18, 18, 19, 19, 20, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 28, 29, 30, 31, 31, 32, 33, 34, 35, 36, 36, 37, 38, 39, 40, 41, 41, 42, 42, 43, 44, 45, 46, 47, 47, 48, 49, 50, 50, 51, 51, 52, 53
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,6


COMMENTS

Also number of primes between prime(n) and n.  Joseph L. Pe, Sep 24 2002
Plot the points (n,a(n)) by, say, appending the line ListPlot[%, PlotJoined > True] to the Mathematica program. The result is virtually a straight line passing through the origin. For the first thousand points, the slope is approximately = 3/4. (This behavior can be explained by using the prime number theorem.)  Joseph L. Pe, Sep 24 2002
Partial sums of A066247, the characteristic function of composites.  ~~~


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000


FORMULA

a(n)=nA000720(n)1=A062298(n)1.


EXAMPLE

Prime(8) = 19 and there are 3 primes between 8 and 19 (endpoints are excluded), namely 11, 13, 17. Hence a(8) = 3.


MATHEMATICA

(*gives number of primes < n*) f[n_] := Module[{r, i}, r = 0; i = 1; While[Prime[i] < n, i++ ]; i  1]; (*gives number of primes between m and n with endpoints excluded*) g[m_, n_] := Module[{r}, r = f[m]  f[n]; If[PrimeQ[n], r = r  1]; r]; Table[g[Prime[n], n], {n, 1, 1000}]
Table[nPrimePi[n]1, {n, 75}] (* Harvey P. Dale, Jun 14 2011 *)
Accumulate[Table[If[CompositeQ[n], 1, 0], {n, 100}]] (* Harvey P. Dale, Sep 24 2016 *)


PROG

(PARI) { for (n=1, 1000, a=n  primepi(n)  1; write("b065855.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 01 2009
(Haskell)
a065855 n = a065855_list !! (n1)
a065855_list = scanl1 (+) (map a066247 [1..])
 Reinhard Zumkeller, Oct 20 2014
(Python)
from sympy import primepi
def A065855(n):
return 0 if n < 4 else n  primepi(n)  1 # Chai Wah Wu, Apr 14 2016


CROSSREFS

Cf. A000720, A062298, A002808.
Cf. A066247.
Sequence in context: A050296 A057062 A255572 * A236863 A242976 A218445
Adjacent sequences: A065852 A065853 A065854 * A065856 A065857 A065858


KEYWORD

easy,nonn,nice


AUTHOR

Labos Elemer, Nov 26 2001


STATUS

approved



