A166061 19-rough numbers: positive integers that have no prime factors less than 19.

1, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271

Offset: 1

Author

Michael B. Porter, Oct 05 2009

Keywords

• easy
• nonn

Comments

Or, positive integers relatively prime to 510510 = 2*3*5*7*11*13*17.

Examples

			437 = 19 * 23 is in the sequence since the two prime factors, 19 and 23, are not less than 19.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Rough Number
• Index entries for sequences related to smooth numbers [From _Michael B. Porter_, Oct 10 2009]

Crossrefs

k-rough numbers: A000027, A005408, A007310, A007775, A008364, A008365, A008366, A166061, A166063.

Programs

Mathematica

Join[{1},Select[Range[300],Min[Transpose[FactorInteger[#]][[1]]]>18&]] (* Harvey P. Dale, Feb 18 2015 *)

PARI

isA166061(n) = gcd(n,510510)==1 \\ Michael B. Porter, Oct 10 2009

Formula

a(n) = k*n + O(1) where k = 17017/3072 = 5.539388.... In particular, k*n - 31 < a(n) < k*n + 25. - Charles R Greathouse IV, Sep 24 2018