A140797 Numbers of the form (2^p^N-1)/(2^p^(N-1)-1), where N>0, p is prime.

3, 5, 7, 17, 31, 73, 127, 257, 2047, 8191, 65537, 131071, 262657, 524287, 1082401, 8388607, 536870911, 2147483647, 4294967297, 137438953471, 2199023255551, 4432676798593, 8796093022207, 140737488355327, 9007199254740991, 18014398643699713, 576460752303423487

Offset: 1

Author

Vladimir Shevelev, Jul 15 2008

Keywords

• nonn

Comments

Contains Fermat numbers A000215 (p=2) and Mersenne numbers A001348 (N=1). The terms of the sequence are either primes A000040 or overpseudoprimes A141232.

The values of A019320(n) for prime power n, sorted. This sequence is a subsequence of A064896, which means that all terms are sturdy numbers (A125121). It appears that the largest prime factor of each of these numbers is a sturdy prime (A143027). - T. D. Noe, Jul 21 2008

Links

• T. D. Noe, Table of n, a(n) for n=1..199
• Vladimir Shevelev, Process of "primoverization" of numbers of the form a^n-1, arXiv:0807.2332 [math.NT], 2008.

Crossrefs

Cf. A000040, A000215, A001348, A141232.

Programs

Mathematica

nmax[p_] := Which[p == 2, 6, p == 3, 4, True, 2];
Reap[Do[If[IntegerQ[k = (2^p^n-1)/(2^p^(n-1)-1)] && k<10^18, Print[{p, n, k}]; Sow[k]], {p, Prime[Range[17]]}, {n, 1, nmax[p]}]][[2, 1]] // Union (* Jean-François Alcover, Dec 10 2018 *)

Extensions

Definition corrected by and more terms from T. D. Noe, Jul 21 2008