OFFSET
1,1
COMMENTS
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
KEYWORD
nonn,fini
AUTHOR
Eric F. O'Brien, Jul 31 2013
STATUS
approved