A330825 Numbers of the form 2^(2^k)*F_k, where F_k is a Fermat prime, A019434.

6, 20, 272, 65792, 4295032832

Offset: 1

Author

Walter Kehowski, Jan 06 2020

Keywords

• nonn

Comments

Also numbers with power-spectral basis {F_n,(F_n-1)^2}. The first element of the power-spectral basis of a(n) is A019434, and the second element is A001146.

Examples

			a(2) = 2^2*(2^2+1) = 20, and the spectral basis of 20 is {5,16}, consisting of primes and powers.
		

Crossrefs

Cf. A000215, A001146, A019434.

Programs

Maple

F := n -> 2^(2^n)+1;
a := proc(n) if isprime(F(n)) then return 2^(2^n)*F(n) fi; end;
[seq(a(n),n=0..4)];

Formula

a(n) = A001146(n-1)*A019434(n), n = 1..5. [Corrected by Georg Fischer, Dec 09 2022]