A330826 Numbers of the form 2^((2^n)+1)*F_n, where F_n is a Fermat prime, A019434.

12, 40, 544, 131584, 8590065664

Offset: 1

Author

Walter Kehowski, Jan 06 2020

Keywords

• nonn
• hard
• more

Comments

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

The first factor of a(n) is 2^A000051(n). The first element of the power-spectral basis of a(n) is A001146, and the second element is A330828.

Examples

			a(2) = 2^(2+1)*5 = 40, and the spectral basis of 40 is {25,16}, consisting of primes and powers.
		

Crossrefs

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

Programs

Maple

F := n -> 2^(2^n)+1;
a := proc(n) if isprime(F(n)) then return 2^((2^n)+1)*F(n) fi; end;

Formula

a(n) =2^A000051(n)*A019434(n).