

A140803


Numbers of the form (2^(p*q)1) /((2^p1)*(2^q1)), where p>q are primes.


3



3, 11, 43, 151, 683, 2359, 2731, 43691, 174763, 599479, 2796203, 8727391, 9588151, 178956971, 715827883, 2454285751, 39268347319, 45812984491, 567767102431, 733007751851, 2932031007403, 10052678938039, 46912496118443, 145295143558111, 3002399751580331, 41175768098368951, 192153584101141163
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OFFSET

1,1


COMMENTS

The sequence contains, in particular, A126614 (q=2) and A143012 (q=3).
If pq1 is squarefree then the terms of the sequence are either primes or overpseudoprimes to base 2 (see A141232). In particular, they are strong pseudoprimes to base 2 (A001262).


LINKS

Robert Israel, Table of n, a(n) for n = 1..825
V. Shevelev, Process of "primoverization" of numbers of the form a^n1, arXiv:0807.2332
S. Wagstaff, Factorizations of 2^n1


EXAMPLE

Entry 3 from (q=2,p=3), entry 11 from (q=2,p=5), entry 43 from (q=2,p=7), entry 151 from (q=3,p=5), entry 683 from (q=2,p=11).


MAPLE

N:= 100: # to use all (p, q) with p*q < N
Primes:= select(isprime, [$2..floor(N/2)]):
A:= {}:
for i from 1 to nops(Primes) do
p:= Primes[i];
Qs:= select(q > q < N/p, [seq(Primes[j], j=1..i1)]);
A:= A union {seq((2^(p*q)1)/(2^p1)/(2^q1), q=Qs)};
od:
A; # Robert Israel, Sep 02 2014


CROSSREFS

Cf. A001262, A141232, A126614, A143012.
Sequence in context: A249568 A106876 A034477 * A246758 A084643 A007583
Adjacent sequences: A140800 A140801 A140802 * A140804 A140805 A140806


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Jul 15 2008, Jul 22 2008; corrected Sep 07 2008


EXTENSIONS

a(17) to a(27) from Robert Israel, Sep 03 2014


STATUS

approved



