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

%I A166063 #25 Feb 16 2025 08:33:11
%S A166063 1,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,
%T A166063 113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,
%U A166063 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 A166063 23-rough numbers: positive integers that have no prime factors less than 23.
%C A166063 Or, positive integers relatively prime to 9699690 = 2*3*5*7*11*13*17*19.
%C A166063 First composite term is 529 = 23^2.
%H A166063 G. C. Greubel, <a href="/A166063/b166063.txt">Table of n, a(n) for n = 1..1200</a>
%H A166063 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RoughNumber.html">Rough Number</a>
%H A166063 <a href="/index/Sk#smooth">Index entries for sequences related to smooth numbers</a>
%F A166063 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 A166063 A166061 SETMINUS A332798 - _R. J. Mathar_, Nov 05 2024
%e A166063 667 = 23 * 29 is in the sequence since the two prime factors, 23 and 29, are not less than 23.
%p A166063 A166063 := proc(n)
%p A166063     option remember;
%p A166063     local a;
%p A166063     if n =1 then
%p A166063         1;
%p A166063     else
%p A166063         for a from procname(n-1)+1 do
%p A166063             numtheory[factorset](a) ;
%p A166063             if min(op(%)) >= 23 then
%p A166063                 return a;
%p A166063             end if;
%p A166063         end do:
%p A166063     end if;
%p A166063 end proc:
%p A166063 seq(A166063(n),n=1..80) ; # _R. J. Mathar_, Nov 05 2024
%t A166063 Select[Range[500],FactorInteger[#][[1,1]]>22&] (* _Harvey P. Dale_, Nov 22 2010 *)
%o A166063 (PARI) isA166063(n) = gcd(n,9699690)==1 \\ _Michael B. Porter_, Oct 10 2009
%Y A166063 k-rough numbers: A000027, A005408, A007310, A007775, A008364, A008365, A008366, A166061, A166063.
%Y A166063 Cf. A332797 (subsequence).
%K A166063 easy,nonn
%O A166063 1,2
%A A166063 _Michael B. Porter_, Oct 05 2009
%E A166063 Additional terms provided provided by _Harvey P. Dale_, Nov 22 2010