A330829 Numbers of the form 2^(2*(2^n)+1)*F_n^2, where F_n is a Fermat prime A019434.

72, 800, 147968, 8657174528, 36894614055915880448

Offset: 0

Author

Walter Kehowski, Jan 06 2020

Keywords

• nonn

Comments

Also numbers with power-spectral basis {(F_n-2)^2*F_n^2,(F_n^2-1)^2}.

The first element of the power-spectral basis of a(n) is A330830, and the second element is A330831. The first factor of a(n) is A000051(n) and the second factor is A330828.

Examples

			a(0) = 2^(2+1)*(2+1)^2 = 72, and the spectral basis is {(3-2)^2*3^2, (3^2-1)^2} = {9,64}, consisting of powers.
		

Crossrefs

Cf. A000215, A001146, A019434, A000051, A330828, A330830, A330831.

Programs

Maple

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

Formula

a(n) = 2^(2*(2^n)+1)*(2^(2^n)+1)^2.