A236128 Primes p such that gpf(gpf(2^p-1)-1) = p.

2, 3, 5, 7, 11, 13, 29, 53

Offset: 1

Author

Thomas Ordowski, Jan 19 2014

Keywords

• nonn
• more

Comments

No more terms found up to p = 1277, 1277 being the first prime for which the complete factorization of 2^p-1 is not currently known (see GIMPS link). - Michel Marcus, Jan 20 2014

Conjecture: gpf(gpf(2^p-1)-1) = p for finitely many p.

Conjecture: gpf(lpf(2^p-1)-1) = p for infinitely many p.

Namely, for p = 2, 3, 5, 7, 11, 13, 23, 29, 37, 43, 47, 53, ... - Michael B. Porter, Jan 26 2014

Note that gpf(lpf(2^p-1)-1) = gpf(gpf(2^p-1)-1) = p for p = 2, 3, 5, 7, 11, 13, 29, 53. See DATA.

Examples

			For prime p=2, 2^p-1=3, gpf(3)=3, gpf(3-1)=2, so 2 is in the sequence.
For prime p=3, 2^p-1=7, gpf(7)=7, gpf(7-1)=3, so 3 is in the sequence.
		

Links

• GIMPS, Exponent Status

Crossrefs

Cf. A003260, A006530.

Programs

Mathematica

Select[Prime[Range[25]], FactorInteger[FactorInteger[2^# - 1][[-1, 1]] - 1][[-1, 1]] == # &] (* Alonso del Arte, Jan 19 2014 *)

PARI

isok(p) = isprime(p) && (q = (vecmax(factor(2^p-1)[,1]))) && (vecmax(factor(q-1)[,1]) == p); \\ Michel Marcus, Jan 19 2014