A152008 Primes which are divisors of numbers of the form (2^phi(3^k) - 1)/3^k.

7, 19, 73, 163, 487, 1459, 2593, 17497, 39367, 52489, 71119, 80191, 87211, 97687, 135433, 139483, 209953, 262657, 379081

Offset: 1

Author

Artur Jasinski, Nov 19 2008

Keywords

• hard
• nonn

Comments

The primes in this sequence have the property that with the exception of 7 they are congruent to 1 mod 18 and with the exception of 7, 19, 73 are congruent to 1 mod 54.

Crossrefs

Cf. A008776, A152007.

Programs

Mathematica

a = {}; Do[k = ((2^EulerPhi[3^(w + 1)] - 1)/3^(w + 1))/((2^EulerPhi[3^w] - 1)/3^w); Do[If[Mod[k, Prime[n]] == 0, AppendTo[a, Prime[n]]; Print[Prime[n]]], {n, PrimePi[2], PrimePi[379081]}], {w, 1, 20}]; Union[a] (*Artur Jasinski*)

Extensions

Edited by N. J. A. Sloane, Nov 26 2008