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%I #28 Sep 08 2022 08:45:14
%S 2,4,6,16,18,22,28,42,58,60,70,72,78,100,102,106,112,148,156,162,190,
%T 210,232,280,310,330,352,358,382,396,448,456,490,568,606,672,756,786,
%U 820,826,828,856,858,876,928,970,982,1008,1012,1030,1068,1092,1108,1150
%N Numbers k such that k^3+1 is an odd semiprime.
%C Numbers n such that n^3 + 1 is a semiprime, because then n^3 + 1 must be odd, since n^3 + 1 = (n+1)*(n^2 - n + 1) is a semiprime only if n+1 is odd. - _Jonathan Sondow_, Feb 02 2014
%C Obviously, n + 1 is always a prime number. Sequence is intersection of A006093 and A055494. - _Altug Alkan_, Dec 20 2015
%H R. J. Mathar, <a href="/A096173/b096173.txt">Table of n, a(n) for n = 1..2086</a>
%F a(n) = 2*A237037(n) = (A237040(n)-1)^(1/3). - _Jonathan Sondow_, Feb 02 2014
%e a(1)=2 because 2^3+1=9=3*3, a(13)=100: 100^3+1=1000001=101*9901.
%p select(n -> isprime(n+1) and isprime(n^2-n+1), [seq(2*i,i=1..1000)]); # _Robert Israel_, Dec 20 2015
%t Select[Range[1200], PrimeQ[#^2 - # + 1] && PrimeQ[# + 1] &] (* _Jonathan Sondow_, Feb 02 2014 *)
%o (PARI) for(n=1, 1e5, if(bigomega(n^3+1)==2, print1(n, ", "))); \\ _Altug Alkan_, Dec 20 2015
%o (Magma) [n: n in [1..2*10^3] | IsPrime(n+1) and IsPrime(n^2-n+1)]; // _Vincenzo Librandi_, Dec 21 2015
%Y Cf. A001358; A081256: largest prime factor of k^3+1; A096174: (k^3+1)/(k+1) is prime; A046315, A237037, A237038, A237039, A237040.
%Y Cf. A006093, A055494.
%K nonn
%O 1,1
%A _Hugo Pfoertner_, Jun 20 2004
%E Corrected by _Zak Seidov_, Mar 08 2006
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