This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A330824 #24 Oct 22 2024 05:43:38
%S A330824 16,64,1024,16384,67108864,17179869184,274877906944,
%T A330824 4611686018427387904,5316911983139663491615228241121378304
%N A330824 Numbers of the form 2^(2*p), where p is a Mersenne exponent, A000043.
%C A330824 Also the second element of the power-spectral basis of A064591. The first element of the power-spectral basis of A064591 is A133049.
%H A330824 Amiram Eldar, <a href="/A330824/b330824.txt">Table of n, a(n) for n = 1..15</a>
%F A330824 a(n) = 2^(2*A000043(n)) = 4^A000043(n).
%e A330824 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 A330824 a := proc(n) if isprime(2^n-1) then return 2^(2*n) fi; end;
%p A330824 [seq(a(n),n=1..31)]; # ithprime(31) = 127
%t A330824 2^(2*MersennePrimeExponent[Range[10]]) (* _Harvey P. Dale_, Jun 27 2023 *)
%o A330824 (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 A330824 Cf. A000043, A000668, A064591, A132794, A133049.
%K A330824 nonn
%O A330824 1,1
%A A330824 _Walter Kehowski_, Jan 06 2020