A227798 Number of composites removed in each step of the Sieve of Eratosthenes for 10^9.

499999999, 166666666, 66666666, 38095237, 20779220, 15984016, 11282834, 9501331, 7435826, 5640969, 5095068, 4131143, 3627360, 3374293, 3015292, 2616982, 2306411, 2192860, 1963654, 1825278, 1750219, 1595163, 1499127, 1381337, 1253379, 1191536

Offset: 1

Author

Eric F. O'Brien, Jul 31 2013

Keywords

• nonn
• fini
• full

Comments

a(n) = the number of composites <= 10^9 for which the n-th prime is the least prime factor.

pi(sqrt(10^9)) = the number of terms of this sequence.

The sum of a(n) for n = 1..3401 = A000720(10^9) + A065855(10^9).

Examples

			a(1) = 10^9 \ 2 - 1.
a(2) = 10^9 \ 3 - 10^9 \ (2*3) - 1
a(3) = 10^9 \ 5 - 10^9 \ (2*5) - 10^9 \ (3*5) + 10^9 \ (2*3*5) - 1
a(4) = 10^9 \ 7 - 10^9 \ (2*7) - 10^9 \ (3*7) - 10^9 \ (5*7) + 10^9 \ (2*3*7) + 10^9 \ (2*5*7) + 10^9 \ (3*5*7) - 10^9 \ (2*3*5*7) - 1.
		

Links

• Eric F. O'Brien, Table of n, a(n) for n = 1..3401

Crossrefs

Cf. A133228, A145538-A145540, A227155, A227797, A227799, A145532-A145537.