A240436 Semiprimes of the form n^3 - 2*n.

4, 21, 115, 329, 2171, 6821, 24331, 50579, 79421, 103729, 226859, 357769, 704791, 1092521, 1224829, 2048129, 2247829, 2685341, 5177371, 6967489, 9393509, 11089121, 12648871, 13651441, 16974079, 25153171, 30663671, 38272079, 46267561, 74617619, 86937421, 90517951

Offset: 1

Author

K. D. Bajpai, Aug 17 2014

Keywords

• nonn
• easy

Comments

Intersection of A001358 and A242135.

Since n^3 - 2*n = n * (n^2 - 2), it follows that n and (n^2 - 2) both should be prime.

Examples

			a(2) = 21: 3^3 - 2*3 = 27 - 6 = 21 = 3 * 7, which is semiprime.
a(3) = 115: 5^3 - 2*5 = 125 - 10 = 115 = 5 * 23, which is semiprime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10545

Crossrefs

Cf. A001358, A062326, A242135, A062326.

Programs

Maple

select(k -> numtheory:-bigomega(k)=2, [seq((n^3-2*n), n=1..500)]);

Mathematica

Select[Table[n^3 - 2*n, {n, 1000}], PrimeOmega[#] == 2 &]

PARI

forprime(p=1,10^3,q=p^2-2;if(isprime(q),print1(p*q,", "))) \\ Derek Orr, Aug 17 2014

Formula

a(n) = A062326(n) * (A062326(n)^2 - 2). - Michel Marcus, Aug 26 2014