

A140797


Numbers of the form (2^p^N1)/(2^p^(N1)1), where N>0, p is prime.


3



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
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OFFSET

1,1


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
V. Shevelev, Process of "primoverization" of numbers of the form a^n1, arxiv:0807.2332


MATHEMATICA

nmax[p_] := Which[p == 2, 6, p == 3, 4, True, 2];
Reap[Do[If[IntegerQ[k = (2^p^n1)/(2^p^(n1)1)] && k<10^18, Print[{p, n, k}]; Sow[k]], {p, Prime[Range[17]]}, {n, 1, nmax[p]}]][[2, 1]] // Union (* JeanFrançois Alcover, Dec 10 2018 *)


CROSSREFS

Cf. A000040 A000215 A001348 A141232.
Sequence in context: A174394 A057476 A016041 * A245730 A038893 A191064
Adjacent sequences: A140794 A140795 A140796 * A140798 A140799 A140800


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Jul 15 2008


EXTENSIONS

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


STATUS

approved



