A330818 - OEIS

%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