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

1,2

Comments

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

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]

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A070299 A159021 A100460 * A224534 A073319 A274048

Adjacent sequences: A166058 A166059 A166060 * A166062 A166063 A166064

Keyword

easy,nonn

Author

Michael B. Porter, Oct 05 2009

Status

approved