cp's OEIS Frontend

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

%I A140797 #14 Mar 14 2023 13:36:35
%S A140797 3,5,7,17,31,73,127,257,2047,8191,65537,131071,262657,524287,1082401,
%T A140797 8388607,536870911,2147483647,4294967297,137438953471,2199023255551,
%U A140797 4432676798593,8796093022207,140737488355327,9007199254740991,18014398643699713,576460752303423487
%N A140797 Numbers of the form (2^p^N-1)/(2^p^(N-1)-1), where N>0, p is prime.
%C A140797 Contains Fermat numbers A000215 (p=2) and Mersenne numbers A001348 (N=1). The terms of the sequence are either primes A000040 or overpseudoprimes A141232.
%C A140797 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
%H A140797 T. D. Noe, <a href="/A140797/b140797.txt">Table of n, a(n) for n=1..199</a>
%H A140797 Vladimir Shevelev, <a href="http://arxiv.org/abs/0807.2332">Process of "primoverization" of numbers of the form a^n-1</a>, arXiv:0807.2332 [math.NT], 2008.
%t A140797 nmax[p_] := Which[p == 2, 6, p == 3, 4, True, 2];
%t A140797 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 *)
%Y A140797 Cf. A000040, A000215, A001348, A141232.
%K A140797 nonn
%O A140797 1,1
%A A140797 _Vladimir Shevelev_, Jul 15 2008
%E A140797 Definition corrected by and more terms from _T. D. Noe_, Jul 21 2008