A166063 - OEIS

%I #25 Feb 16 2025 08:33:11

%S 1,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,

%T 113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,

%U 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

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

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

%C First composite term is 529 = 23^2.

%H G. C. Greubel, <a href="/A166063/b166063.txt">Table of n, a(n) for n = 1..1200</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RoughNumber.html">Rough Number</a>

%H <a href="/index/Sk#smooth">Index entries for sequences related to smooth numbers</a>

%F 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

%F A166061 SETMINUS A332798 - _R. J. Mathar_, Nov 05 2024

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

%p A166063 := proc(n)

%p     option remember;

%p     local a;

%p     if n =1 then

%p         1;

%p     else

%p         for a from procname(n-1)+1 do

%p             numtheory[factorset](a) ;

%p             if min(op(%)) >= 23 then

%p                 return a;

%p             end if;

%p         end do:

%p     end if;

%p end proc:

%p seq(A166063(n),n=1..80) ; # _R. J. Mathar_, Nov 05 2024

%t Select[Range[500],FactorInteger[#][[1,1]]>22&] (* _Harvey P. Dale_, Nov 22 2010 *)

%o (PARI) isA166063(n) = gcd(n,9699690)==1 \\ _Michael B. Porter_, Oct 10 2009

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

%Y Cf. A332797 (subsequence).

%K easy,nonn

%O 1,2

%A _Michael B. Porter_, Oct 05 2009

%E Additional terms provided provided by _Harvey P. Dale_, Nov 22 2010