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A140803 Numbers of the form (2^(p*q)-1) /((2^p-1)*(2^q-1)), 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence contains, in particular, A126614 (q=2) and A143012 (q=3).

If pq-1 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^n-1, arXiv:0807.2332

S. Wagstaff, Factorizations of 2^n-1

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..i-1)]);

  A:= A union {seq((2^(p*q)-1)/(2^p-1)/(2^q-1), 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

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Last modified December 2 23:29 EST 2016. Contains 278694 sequences.