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

0,1

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.

Links

Table of n, a(n) for n=0..4.

Formula

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

Example

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.

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)];

Crossrefs

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

Sequence in context: A086579 A113855 A082949 * A240983 A210627 A019562

Adjacent sequences: A330826 A330827 A330828 * A330830 A330831 A330832

Keyword

nonn

Author

Walter Kehowski, Jan 06 2020

Status

approved