A227797 - OEIS

%I #15 Aug 22 2019 02:38:05

%S 49999999,16666666,6666666,3809523,2077920,1598400,1128284,950133,

%T 743581,564099,509508,413103,362709,337382,301484,261684,230683,

%U 219393,196552,182782,175351,159910,150351,138581,125778,119552,116075,110630,107564,102739,90485

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

%C The number of composites <= 10^8 for which the n-th prime is the least prime factor.

%C pi(sqrt(10^8)) = the number of terms of A227797.

%C The sum of a(n) for n = 1..1229 = A000720(10^8) + A065855(10^8).

%H Eric F. O'Brien, <a href="/A227797/b227797.txt">Table of n, a(n) for n = 1..1229</a>

%F Writing floor(a/b) as [a / b]:

%F a(1) = [10^8 / 2] - 1.

%F a(2) = [10^8 / 3] - [10^8 / 6] - 1.

%F a(3) = [10^8 / 5] - [10^8 / 10] - [10^8 / 15] + [10^8 / 30] - 1.

%F 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 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 Cf. A133228, A145538-A145540, A227155, A227798, A227799, A145532-A145537.

%K nonn,fini

%O 1,1

%A _Eric F. O'Brien_, Jul 31 2013