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Twice Mersenne primes A000668(n).
7

%I #25 Oct 21 2024 04:36:17

%S 6,14,62,254,16382,262142,1048574,4294967294,4611686018427387902,

%T 1237940039285380274899124222,324518553658426726783156020576254,

%U 340282366920938463463374607431768211454

%N Twice Mersenne primes A000668(n).

%C Radicals of even perfect numbers. - _Charles R Greathouse IV_, Feb 01 2013

%H Amiram Eldar, <a href="/A139257/b139257.txt">Table of n, a(n) for n = 1..18</a>

%H Florian Luca and Carl Pomerance, <a href="http://nyjm.albany.edu/j/2010/16-3.html">On the radical of a perfect number</a>, New York Journal of Math., 16 (2010), 23-30; <a href="http://www.math.dartmouth.edu/~carlp/LucaPomeranceNYJMstyle.pdf">alternative link</a>.

%F a(n) = 2*A000668(n).

%F a(n) = A000918(1 + A000043(n)) = A095121(A000043(n)). - _Omar E. Pol_, Jun 07 2012

%t 2*(2^MersennePrimeExponent[Range[15]]-1) (* _Harvey P. Dale_, Jan 05 2020 *)

%o (PARI) apply(p->2*(2^p-1),select(p->ispseudoprime(2^p-1),primes(40))) \\ _Charles R Greathouse IV_, Feb 01 2013

%Y Cf. A000043, A000668, A000918, A060590, A095121, A100484, A139256.

%K nonn

%O 1,1

%A _Omar E. Pol_, Apr 23 2008

%E Corrected and extended by _Joerg Arndt_, Jun 07 2012.