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A227155 Number of composites removed in each step of the Sieve of Eratosthenes for 10^7. 4

%I

%S 4999999,1666666,666666,380952,207791,159839,112829,95016,74356,56405,

%T 50949,41317,36293,33780,30205,26228,23123,21975,19655,18249,17467,

%U 15871,14876,13668,12358,11710,11344,10779,10451,9955,8748,8398,7956,7768,7181,7034,6724

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

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

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

%C 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)).

%H Eric F. O'Brien, <a href="/A227155/b227155.txt">Table of n, a(n) for n = 1..446</a>

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

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

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

%e For n = 2, prime(n) = 3, a(n) = 1666666: 3 divides 10^7 3333333 times.

%e 6 is the common multiple of 2 and 3, thus 10^7 \ 6 multiples of 3 (1666666) have already been eliminated by a(1).

%e 3333333 less 1666666 = 1666667, less 1 because 3 itself is not eliminated.

%e Thus a(2) = 3333333 - 1666666 - 1 = 1666666.

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

%K nonn,fini

%O 1,1

%A _Eric F. O'Brien_, Jul 02 2013

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Last modified May 6 13:04 EDT 2021. Contains 343585 sequences. (Running on oeis4.)