A231815 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.

30, 51319, 3882139, 289022911, 674910259, 991523479, 1893583519, 4550912389, 9761467669, 16721570539, 28685399311, 72886214809, 77372307511, 82720376839, 98685849571, 173850108931, 220038912319, 229352039821, 240313142749, 257401051861, 428178002569

Offset: 1

Author

Jaroslav Krizek, Nov 13 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.

These numbers are divisible by the arithmetic mean of their proper divisors.

Examples

			3882139 = 79*157*313; 157 = 2*79 - 1; 313 = 2*157 - 1.
		

Links

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

Crossrefs

Cf. A005117, A057326, A000040, A231814, A231816.

Cf. A057326 (first member of a prime triple in a 2p-1 progression).

Programs

Mathematica

t = {}; p = 1; Do[While[p = NextPrime[p]; ! (PrimeQ[p2 = 2 p - 1] && PrimeQ[p3 = 2 p2 - 1])]; AppendTo[t, p*p2*p3], {30}]; t (* T. D. Noe, Nov 15 2013 *)
3#-10#^2+8#^3&/@Select[Prime[Range[600]],AllTrue[{2#-1,4#-3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 02 2016 *)