OFFSET
3,3
COMMENTS
Primes are known as primes actually one step before a(n): at step k of the sieve, multiples of prime(k) are removed, the smallest integer removed being prime(k)^2; every remaining integer less than prime(k+1)^2 will then never be removed, and it is newly known at step k for those between prime(k)^2 and prime(k+1)^2. For example, at step 3, multiples of prime(3) = 5 are removed and remaining integers after this step are prime up to prime(4)^2 = 49; then, 29, 31, 37, 41, 43, 47 are known as prime at step 3. - Jean-Christophe Hervé, Nov 01 2013
LINKS
T. D. Noe, Table of n, a(n) for n = 3..10000
H. B. Meyer, Eratosthenes' sieve
J. Britton, Sieve of Eratosthenes Applet
C. K. Caldwell, The Prime Glossary, Sieve of Eratosthenes
Wikipedia, Sieve of Eratosthenes
FORMULA
If n is composite, a(n) = A055396(n); if n is prime, a(n) = A056811(n)+1. [Corrected by Charles R Greathouse IV, Sep 03 2013]
EXAMPLE
a(7)=2 because 7 is not removed by the first two stages of the sieve, but is less than the square of the second prime (though not the square of the first); a(35)=3 because 35 is removed in the third stage as a multiple of 5.
MATHEMATICA
a[n_ /; !PrimeQ[n]] := PrimePi[ FactorInteger[n][[1, 1]]]; a[n_ /; PrimeQ[n]] := PrimePi[ NextPrime[ Sqrt[n]]]; Table[a[n], {n, 3, 107}](* Jean-François Alcover, Jun 11 2012, after formula *)
CROSSREFS
KEYWORD
nice,nonn,easy
AUTHOR
Henry Bottomley, May 15 2000
STATUS
approved