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Numbers of the form k^2+k+1 that are the product of two distinct primes.
3

%I #15 Jan 25 2024 04:51:47

%S 21,57,91,111,133,183,381,553,703,813,871,993,1057,1191,1261,1333,

%T 1561,1641,1807,1893,1981,2071,2257,2353,2653,2757,2863,3193,3661,

%U 4033,4291,4971,5257,5403,5853,6807,6973,7141,7311,7483,8373,8557,8743,9121,9313,9507,9703

%N Numbers of the form k^2+k+1 that are the product of two distinct primes.

%H David A. Corneth, <a href="/A176069/b176069.txt">Table of n, a(n) for n = 1..10000</a>

%e 21 is a term as 21 = 3*7 = 4^2+4+1; 21 is the product of two distinct primes and 21 is of the form k^2 + k + 1.

%t f[n_]:=Last/@FactorInteger[n]=={1,1};Select[Array[ #^2+#+1&,6!,2],f[ # ]&]

%Y Cf. A002061, A006881, A174969.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 07 2010

%E Name corrected by _David A. Corneth_, May 29 2023