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A332797 Numbers whose smallest prime factor is 23.

%I A332797 #23 Aug 29 2025 16:42:26
%S A332797 23,529,667,713,851,943,989,1081,1219,1357,1403,1541,1633,1679,1817,
%T A332797 1909,2047,2231,2323,2369,2461,2507,2599,2921,3013,3151,3197,3427,
%U A332797 3473,3611,3749,3841,3979,4117,4163,4393,4439,4531,4577,4853,5129,5221,5267,5359,5497
%N A332797 Numbers whose smallest prime factor is 23.
%C A332797 The asymptotic density of this sequence is 55296/7436429. - _Amiram Eldar_, Dec 06 2020
%D A332797 Emmanuel Desurvire, Classical and Quantum Information Theory: An Introduction for the Telecom Scientist, Cambridge University Press, 2009, table 20.5 p. 421.
%H A332797 Amiram Eldar, <a href="/A332797/b332797.txt">Table of n, a(n) for n = 1..10000</a>
%F A332797 a(n) = 23*A166063(n).
%e A332797 a(2) = 23*23, a(3) = 23*29.
%t A332797 23 * Select[Range[240], CoprimeQ[#, 9699690] &] (* _Amiram Eldar_, Feb 24 2020 *)
%t A332797 Select[Range[6000],FactorInteger[#][[1,1]]==23&] (* _Harvey P. Dale_, Aug 29 2025 *)
%o A332797 (Rexx)
%o A332797 P = 23         ;  S = P
%o A332797 do N = P by 2 while length( S ) < 255
%o A332797    do I = 1 until P = X
%o A332797       X = PRIME( I )
%o A332797       if P = X       then  leave I
%o A332797       if N // X = 0  then  iterate N
%o A332797    end I
%o A332797    S = S || ',' P*N
%o A332797 end N
%o A332797 say S          ;  return S
%Y A332797 Cf. A084967 (5), A084968 (7), A084969 (11), A084970 (13), A332799 (17), A332798 (19), A166063 (23-rough numbers).
%K A332797 nonn,easy,changed
%O A332797 1,1
%A A332797 _Frank Ellermann_, Feb 24 2020