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 A096173 Numbers k such that k^3+1 is an odd semiprime. 19
 2, 4, 6, 16, 18, 22, 28, 42, 58, 60, 70, 72, 78, 100, 102, 106, 112, 148, 156, 162, 190, 210, 232, 280, 310, 330, 352, 358, 382, 396, 448, 456, 490, 568, 606, 672, 756, 786, 820, 826, 828, 856, 858, 876, 928, 970, 982, 1008, 1012, 1030, 1068, 1092, 1108, 1150 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 Obviously, n + 1 is always a prime number. Sequence is intersection of A006093 and A055494. - Altug Alkan, Dec 20 2015 LINKS R. J. Mathar, Table of n, a(n) for n = 1..2086 FORMULA a(n) = 2*A237037(n) = (A237040(n)-1)^(1/3). - Jonathan Sondow, Feb 02 2014 EXAMPLE a(1)=2 because 2^3+1=9=3*3, a(13)=100: 100^3+1=1000001=101*9901. MAPLE select(n -> isprime(n+1) and isprime(n^2-n+1), [seq(2*i, i=1..1000)]); # Robert Israel, Dec 20 2015 MATHEMATICA Select[Range, PrimeQ[#^2 - # + 1] && PrimeQ[# + 1] &] (* Jonathan Sondow, Feb 02 2014 *) PROG (PARI) for(n=1, 1e5, if(bigomega(n^3+1)==2, print1(n, ", "))); \\ Altug Alkan, Dec 20 2015 (MAGMA) [n: n in [1..2*10^3] | IsPrime(n+1) and IsPrime(n^2-n+1)]; // Vincenzo Librandi, Dec 21 2015 CROSSREFS Cf. A001358; A081256: largest prime factor of k^3+1; A096174: (k^3+1)/(k+1) is prime; A046315, A237037, A237038, A237039, A237040. Cf. A006093, A055494. Sequence in context: A341668 A326782 A096174 * A287681 A333021 A114874 Adjacent sequences:  A096170 A096171 A096172 * A096174 A096175 A096176 KEYWORD nonn AUTHOR Hugo Pfoertner, Jun 20 2004 EXTENSIONS Corrected by Zak Seidov, Mar 08 2006 STATUS approved

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Last modified April 21 13:04 EDT 2021. Contains 343153 sequences. (Running on oeis4.)