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Numbers whose smallest prime factor is 19.
7

%I #21 Sep 06 2023 13:41:01

%S 19,361,437,551,589,703,779,817,893,1007,1121,1159,1273,1349,1387,

%T 1501,1577,1691,1843,1919,1957,2033,2071,2147,2413,2489,2603,2641,

%U 2831,2869,2983,3097,3173,3287,3401,3439,3629,3667,3743,3781,4009,4237,4313,4351,4427

%N Numbers whose smallest prime factor is 19.

%C The asymptotic density of this sequence is 3072/323323. - _Amiram Eldar_, Dec 06 2020

%D Emmanuel Desurvire, Classical and Quantum Information Theory: An Introduction for the Telecom Scientist, Cambridge University Press, 2009, table 20.5 p. 421.

%H Amiram Eldar, <a href="/A332798/b332798.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 19*A166061(n).

%e a(2) = 19*19, a(3) = 19*23.

%t 19 * Select[Range[235], CoprimeQ[#, 510510] &] (* _Amiram Eldar_, Feb 24 2020 *)

%o (Rexx)

%o P = 19 ; S = P

%o do N = P by 2 while length( S ) < 255

%o do I = 1 until P = X

%o X = PRIME( I )

%o if P = X then leave I

%o if N // X = 0 then iterate N

%o end I

%o S = S || ',' P*N

%o end N

%o say S ; return S

%Y Cf. A084967 (5), A084968 (7), A084969 (11), A084970 (13), A332799 (17), A332797 (23), A166061 (19-rough numbers).

%K nonn,easy

%O 1,1

%A _Frank Ellermann_, Feb 24 2020