A227155 Number of composites removed in each step of the Sieve of Eratosthenes for 10^7.

4999999, 1666666, 666666, 380952, 207791, 159839, 112829, 95016, 74356, 56405, 50949, 41317, 36293, 33780, 30205, 26228, 23123, 21975, 19655, 18249, 17467, 15871, 14876, 13668, 12358, 11710, 11344, 10779, 10451, 9955, 8748, 8398, 7956, 7768, 7181, 7034, 6724

Offset

1,1

Comments

The number of composites <= 10^7 for which the n-th prime is the least prime factor.

The number of multiples of the n-th prime <= 10^7 that do not have any prime < the n-th prime as a factor.

The greatest n for which the n-th prime is a multiple <= 10^7 without a prime factor < n-th prime = primepi(sqrt(10^7)).

Links

Eric F. O'Brien, Table of n, a(n) for n = 1..446

Formula

a(1) = 10^7 \ 2 - 1.

a(2) = 10^7 \ 3 - 10^7 \ 6 - 1.

a(3) = 10^7 \ 5 - 10^7 \ 10 - 10^7 \ 15 + 10^7 \ 30 - 1.

Example

For n = 2, prime(n) = 3, a(n) = 1666666: 3 divides 10^7 3333333 times.
6 is the common multiple of 2 and 3, thus 10^7 \ 6 multiples of 3 (1666666) have already been eliminated by a(1).
3333333 less 1666666 = 1666667, less 1 because 3 itself is not eliminated.
Thus a(2) = 3333333 - 1666666 - 1 = 1666666.

Crossrefs

Cf. A133228, A145540, A145538, A145539, A145532-A145537.

Sequence in context: A151646 A210318 A359296 * A106785 A034607 A015363

Adjacent sequences: A227152 A227153 A227154 * A227156 A227157 A227158

Keyword

nonn,fini

Author

Eric F. O'Brien, Jul 02 2013

Status

approved