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

1,2

Comments

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

First composite term is 529 = 23^2.

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

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

Example

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

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 *)

Prog

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

Crossrefs

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

Cf. A332797 (subsequence).

Sequence in context: A255220 A060703 A061753 * A231073 A049483 A112681

Adjacent sequences: A166060 A166061 A166062 * A166064 A166065 A166066

Keyword

easy,nonn

Author

Michael B. Porter, Oct 05 2009

Extensions

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

Status

approved