A330824 - OEIS

%I #19 Jun 27 2023 17:23:34

%S 16,64,1024,16384,67108864,17179869184,274877906944,

%T 4611686018427387904,5316911983139663491615228241121378304

%N Numbers of the form 2^(2*p), where p is a Mersenne exponent, A000043.

%C Also the second element of the power-spectral basis of A064591. The first element of the power-spectral basis of A064591 is A133049.

%F a(n) = 2^(2*A000043(n)) = 4^A000043(n).

%e a(1) = 2^(2*2) = 16. Also A133049(1) = 3^2 = 9, and the spectral basis of A064591(1) = 24 is {9, 16}, consisting of primes and powers.

%p a := proc(n) if isprime(2^n-1) then return 2^(2*n) fi; end;

%p [seq(a(n),n=1..31)]; # ithprime(31) = 127

%t 2^(2*MersennePrimeExponent[Range[10]]) (* _Harvey P. Dale_, Jun 27 2023 *)

%o (PARI) forprime(p=1,99,isprime(2^p-1)&&print1(4^p",")) \\ or better: {A330824(n)=4^A000043(n)}. - _M. F. Hasler_, Feb 07 2020

%Y Cf. A000043, A000668, A064591, A132794, A133049.

%K nonn

%O 1,1

%A _Walter Kehowski_, Jan 06 2020