A332798 Numbers whose smallest prime factor is 19.

19, 361, 437, 551, 589, 703, 779, 817, 893, 1007, 1121, 1159, 1273, 1349, 1387, 1501, 1577, 1691, 1843, 1919, 1957, 2033, 2071, 2147, 2413, 2489, 2603, 2641, 2831, 2869, 2983, 3097, 3173, 3287, 3401, 3439, 3629, 3667, 3743, 3781, 4009, 4237, 4313, 4351, 4427

Offset: 1

Author

Frank Ellermann, Feb 24 2020

Keywords

• nonn
• easy

Comments

The asymptotic density of this sequence is 3072/323323. - Amiram Eldar, Dec 06 2020

Examples

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

References

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

19 * Select[Range[235], CoprimeQ[#, 510510] &] (* Amiram Eldar, Feb 24 2020 *)

Rexx

P = 19         ;  S = P
do N = P by 2 while length( S ) < 255
   do I = 1 until P = X
      X = PRIME( I )
      if P = X       then  leave I
      if N // X = 0  then  iterate N
   end I
   S = S || ',' P*N
end N
say S          ;  return S

Formula

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