A259189 Semiprimes of the form n^3 + 2.

10, 218, 514, 731, 1333, 2199, 2746, 3377, 4915, 5834, 6861, 8002, 9263, 12169, 15627, 29793, 35939, 42877, 54874, 59321, 68923, 117651, 125002, 132653, 148879, 185195, 205381, 314434, 405226, 421877, 474554, 531443, 592706, 658505, 704971

Offset: 1

Author

Morris Neene, Jun 20 2015

Keywords

• nonn

Comments

Intersection of A001358 and A084380. - Michel Marcus, Jun 20 2015

Since there are no squares of the form n^3 + 2, all semiprimes in this sequence are products of distinct primes.

No term in A040034 divides any term in this sequence.

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358 (semiprimes), A084380 (n^3+2), A144953 (primes of same form).

Cf. A237040 (similar sequence with n^3+1).

Programs

Magma

IsSP:=func;[r:n in [1..1000]|IsSP(r) where r is 2+n^3];

Mathematica

Select[Range[100]^3 + 2, PrimeOmega[#] == 2 &] (* Alonso del Arte, Jun 20 2015 *)

PARI

is(n)=bigomega(n^3 + 2)==2 \\ Anders Hellström, Sep 07 2015

Perl

use ntheory ":all"; my @sp = grep { scalar(factor($))==2 } map { $**3+2 } 1..100; say "@sp"; # Dana Jacobsen, Sep 07 2015