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 A330829 Numbers of the form 2^(2*(2^n)+1)*F_n^2, where F_n is a Fermat prime A019434. 3
 72, 800, 147968, 8657174528, 36894614055915880448 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified August 13 22:26 EDT 2020. Contains 336464 sequences. (Running on oeis4.)