cp's OEIS Frontend

A227797 Number of composites removed in each step in the Sieve of Eratosthenes for 10^8.

%I A227797 #15 Aug 22 2019 02:38:05
%S A227797 49999999,16666666,6666666,3809523,2077920,1598400,1128284,950133,
%T A227797 743581,564099,509508,413103,362709,337382,301484,261684,230683,
%U A227797 219393,196552,182782,175351,159910,150351,138581,125778,119552,116075,110630,107564,102739,90485
%N A227797 Number of composites removed in each step in the Sieve of Eratosthenes for 10^8.
%C A227797 The number of composites <= 10^8 for which the n-th prime is the least prime factor.
%C A227797 pi(sqrt(10^8)) = the number of terms of A227797.
%C A227797 The sum of a(n) for n = 1..1229 = A000720(10^8) + A065855(10^8).
%H A227797 Eric F. O'Brien, <a href="/A227797/b227797.txt">Table of n, a(n) for n = 1..1229</a>
%F A227797 Writing floor(a/b) as [a / b]:
%F A227797 a(1) = [10^8 / 2] - 1.
%F A227797 a(2) = [10^8 / 3] - [10^8 / 6] - 1.
%F A227797 a(3) = [10^8 / 5] - [10^8 / 10] - [10^8 / 15] + [10^8 / 30] - 1.
%F A227797 a(4) = [10^8 / 7] - [10^8 / 14] - [10^8 / 21] - [10^8 / 35] + [10^8 / 42] + [10^8 / 70] + [10^8 / 105] - [10^8 / 210] - 1.
%e A227797 For n = 3, prime(n) = 5, a(n) = 6666666: 5 divides 10^8 20000000 times. 10 is the least common multiple of 2 (prime(1)) and 5 and 15 is the least common multiple of 3 (prime(2)) and 5; thus [10^8 / 10] multiples of 5 and [10^8 / 15] multiples of 5 have already been eliminated by a(1) and a(2), and thereby respectively reduce a(3) by 10000000 and 6666666 offset by [10^8 / 30] multiples of 5 which would otherwise excessively reduce a(3) by 3333333 because 30 is the least common multiple of 2, 3 and 5. a(3) is further reduced by 1 as 5 itself is not eliminated.
%Y A227797 Cf. A133228, A145538-A145540, A227155, A227798, A227799, A145532-A145537.
%K A227797 nonn,fini
%O A227797 1,1
%A A227797 _Eric F. O'Brien_, Jul 31 2013