A166063 23-rough numbers: positive integers that have no prime factors less than 23.

1, 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, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499

Offset: 1

Author

Michael B. Porter, Oct 05 2009

Keywords

• easy
• nonn

Comments

Or, positive integers relatively prime to 9699690 = 2*3*5*7*11*13*17*19.

First composite term is 529 = 23^2.

Examples

			667 = 23 * 29 is in the sequence since the two prime factors, 23 and 29, are not less than 23.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1200
• Eric Weisstein's World of Mathematics, Rough Number
• Index entries for sequences related to smooth numbers

Crossrefs

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

Cf. A332797 (subsequence).

Programs

Maple

A166063 := proc(n)
    option remember;
    local a;
    if n =1 then
        1;
    else
        for a from procname(n-1)+1 do
            numtheory[factorset](a) ;
            if min(op(%)) >= 23 then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A166063(n),n=1..80) ; # R. J. Mathar, Nov 05 2024

Mathematica

Select[Range[500],FactorInteger[#][[1,1]]>22&] (* Harvey P. Dale, Nov 22 2010 *)

PARI

isA166063(n) = gcd(n,9699690)==1 \\ Michael B. Porter, Oct 10 2009

Formula

a(n) = k*n + O(1) where k = 323323/55296 = 5.8471.... In particular, k*n - 51 < a(n) < k*n + 45. - Charles R Greathouse IV, Sep 21 2018

A166061 SETMINUS A332798 - R. J. Mathar, Nov 05 2024

Extensions

Additional terms provided provided by Harvey P. Dale, Nov 22 2010