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Numbers whose smallest prime factor is 23.
7

%I #21 Sep 06 2023 13:41:22

%S 23,529,667,713,851,943,989,1081,1219,1357,1403,1541,1633,1679,1817,

%T 1909,2047,2231,2323,2369,2461,2507,2599,2921,3013,3151,3197,3427,

%U 3473,3611,3749,3841,3979,4117,4163,4393,4439,4531,4577,4853,5129,5221,5267,5359,5497

%N Numbers whose smallest prime factor is 23.

%C The asymptotic density of this sequence is 55296/7436429. - _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="/A332797/b332797.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 23*A166063(n).

%e a(2) = 23*23, a(3) = 23*29.

%t 23 * Select[Range[240], CoprimeQ[#, 9699690] &] (* _Amiram Eldar_, Feb 24 2020 *)

%o (Rexx)

%o P = 23 ; 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), A332798 (19), A166063 (23-rough numbers).

%K nonn,easy

%O 1,1

%A _Frank Ellermann_, Feb 24 2020