A330824 Numbers of the form 2^(2*p), where p is a Mersenne exponent, A000043.

16, 64, 1024, 16384, 67108864, 17179869184, 274877906944, 4611686018427387904, 5316911983139663491615228241121378304

Offset: 1

Author

Walter Kehowski, Jan 06 2020

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..15

Crossrefs

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

Programs

Maple

a := proc(n) if isprime(2^n-1) then return 2^(2*n) fi; end;
[seq(a(n),n=1..31)]; # ithprime(31) = 127

Mathematica

2^(2*MersennePrimeExponent[Range[10]]) (* Harvey P. Dale, Jun 27 2023 *)

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

Formula

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