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A332798 Numbers whose smallest prime factor is 19.

%I A332798 #21 Sep 06 2023 13:41:01
%S A332798 19,361,437,551,589,703,779,817,893,1007,1121,1159,1273,1349,1387,
%T A332798 1501,1577,1691,1843,1919,1957,2033,2071,2147,2413,2489,2603,2641,
%U A332798 2831,2869,2983,3097,3173,3287,3401,3439,3629,3667,3743,3781,4009,4237,4313,4351,4427
%N A332798 Numbers whose smallest prime factor is 19.
%C A332798 The asymptotic density of this sequence is 3072/323323. - _Amiram Eldar_, Dec 06 2020
%D A332798 Emmanuel Desurvire, Classical and Quantum Information Theory: An Introduction for the Telecom Scientist, Cambridge University Press, 2009, table 20.5 p. 421.
%H A332798 Amiram Eldar, <a href="/A332798/b332798.txt">Table of n, a(n) for n = 1..10000</a>
%F A332798 a(n) = 19*A166061(n).
%e A332798 a(2) = 19*19, a(3) = 19*23.
%t A332798 19 * Select[Range[235], CoprimeQ[#, 510510] &] (* _Amiram Eldar_, Feb 24 2020 *)
%o A332798 (Rexx)
%o A332798 P = 19         ;  S = P
%o A332798 do N = P by 2 while length( S ) < 255
%o A332798    do I = 1 until P = X
%o A332798       X = PRIME( I )
%o A332798       if P = X       then  leave I
%o A332798       if N // X = 0  then  iterate N
%o A332798    end I
%o A332798    S = S || ',' P*N
%o A332798 end N
%o A332798 say S          ;  return S
%Y A332798 Cf. A084967 (5), A084968 (7), A084969 (11), A084970 (13), A332799 (17), A332797 (23), A166061 (19-rough numbers).
%K A332798 nonn,easy
%O A332798 1,1
%A A332798 _Frank Ellermann_, Feb 24 2020