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%I #21 Jan 07 2020 22:52:53
%S 32,128,2048,32768,134217728,34359738368,549755813888,
%T 9223372036854775808,10633823966279326983230456482242756608,
%U 766247770432944429179173513575154591809369561091801088
%N Numbers of the form 2^(2*p+1), where p is a Mersenne exponent, A000043.
%C Also the first factor of A330817, 2^(2*p+1)*M_p^2. The second factor of A330817 is A133049.
%H Walter Kehowski, <a href="/A330818/b330818.txt">Table of n, a(n) for n = 1..12</a>
%F a(n) = 2^(2*A000043(n)+1).
%e a(1) = 2^(2*2+1) = 32. Since M_2=3, the number 2^5*3^2 has power-spectral basis {225,64}.
%p A330818:=[]:
%p for www to 1 do
%p for i from 1 to 31 do
%p #ithprime(31)=127
%p p:=ithprime(i);
%p q:=2^p-1;
%p if isprime(q) then x:=2^(2*p+1); A330818:=[op(A330818),x]; fi;
%p od;
%p od;
%p A330818;
%t 2^(2 * MersennePrimeExponent[Range[10]] + 1) (* _Amiram Eldar_, Jan 03 2020 *)
%Y Cf. A000043, A000668, A132794, A133049, A330817, A330819, A330820.
%K nonn
%O 1,1
%A _Walter Kehowski_, Jan 01 2020
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