

A227797


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


3



49999999, 16666666, 6666666, 3809523, 2077920, 1598400, 1128284, 950133, 743581, 564099, 509508, 413103, 362709, 337382, 301484, 261684, 230683, 219393, 196552, 182782, 175351, 159910, 150351, 138581, 125778, 119552, 116075, 110630, 107564, 102739, 90485
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OFFSET

1,1


COMMENTS

The number of composites <= 10^8 for which the nth prime is the least prime factor.
pi(sqrt(10^8)) = the number of terms of A227797.
The sum of a(n) for n = 1..1229 = A000720(10^8) + A065855(10^8).


LINKS

Eric F. O'Brien, Table of n, a(n) for n = 1..1229


FORMULA

Writing floor(a/b) as [a / b]:
a(1) = [10^8 / 2]  1.
a(2) = [10^8 / 3]  [10^8 / 6]  1.
a(3) = [10^8 / 5]  [10^8 / 10]  [10^8 / 15] + [10^8 / 30]  1.
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.


EXAMPLE

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.


CROSSREFS

Cf. A133228, A145538A145540, A227155, A227798, A227799, A145532A145537.
Sequence in context: A017459 A017591 A271020 * A236947 A080796 A068242
Adjacent sequences: A227794 A227795 A227796 * A227798 A227799 A227800


KEYWORD

nonn,fini


AUTHOR

Eric F. O'Brien, Jul 31 2013


STATUS

approved



