cp's OEIS Frontend

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

%I A227155 #9 Jul 12 2013 13:42:13
%S A227155 4999999,1666666,666666,380952,207791,159839,112829,95016,74356,56405,
%T A227155 50949,41317,36293,33780,30205,26228,23123,21975,19655,18249,17467,
%U A227155 15871,14876,13668,12358,11710,11344,10779,10451,9955,8748,8398,7956,7768,7181,7034,6724
%N A227155 Number of composites removed in each step of the Sieve of Eratosthenes for 10^7.
%C A227155 The number of composites <= 10^7 for which the n-th prime is the least prime factor.
%C A227155 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 A227155 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 A227155 Eric F. O'Brien, <a href="/A227155/b227155.txt">Table of n, a(n) for n = 1..446</a>
%F A227155 a(1) = 10^7 \ 2 - 1.
%F A227155 a(2) = 10^7 \ 3 - 10^7 \ 6 - 1.
%F A227155 a(3) = 10^7 \ 5 - 10^7 \ 10 - 10^7 \ 15 + 10^7 \ 30 - 1.
%e A227155 For n = 2, prime(n) = 3, a(n) = 1666666: 3 divides 10^7 3333333 times.
%e A227155 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 A227155 3333333 less 1666666 = 1666667, less 1 because 3 itself is not eliminated.
%e A227155 Thus a(2) = 3333333 - 1666666 - 1 = 1666666.
%Y A227155 Cf. A133228, A145540, A145538, A145539, A145532-A145537.
%K A227155 nonn,fini
%O A227155 1,1
%A A227155 _Eric F. O'Brien_, Jul 02 2013