A231967 Squarefree numbers (A005117) of the form p*q*r with prime factors p, q, r with q = 2*p + 1 and r = 2*q + 1.

110, 1265, 11891, 568301, 5719229, 46203659, 371436119, 1057570169, 2978731439, 8475105539, 8777935031, 14865764009, 22397944469, 24460553171, 26008879181, 27621202391, 47549400491, 53960155829, 54994829321, 57639193331, 119010782819, 157361958899

Offset: 1

Author

Jaroslav Krizek, Nov 16 2013

Keywords

• nonn

Comments

Squarefree numbers of the form p*q*r, where p < q < r = primes with q = 2*p + 1 and r = 2*q + 1; that is, r = 4*p + 3.

Examples

			5719229 = 89*179*359, 179 = 2*89 + 1, 359 = 2*179 + 1.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005117, A000040, A231968, A231969, A231966. Cf. A007700 (first member of a prime triple in a 2p+1 progression).

Programs

Mathematica

sfQ[n_]:=Module[{q=2n+1,r},r=2q+1;AllTrue[{q,r},PrimeQ]&& SquareFreeQ[ n*q*r]]; 3#+10#^2+8#^3&/@Select[Prime[Range[400]],sfQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 26 2016 *)