This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(1) = 3^2 = 9. The spectral basis of A330826(1) = 12 is {9,4}, consisting of primes and powers.
F := n -> 2^(2^n) + 1; a := proc(n) if isprime(F(n)) then return F(n)^2 fi; end; [seq(a(n)),n=0..4)];
(2^2^Select[Range[0,5],PrimeQ[2^(2^#)+1] &]+1)^2 (* Stefano Spezia, May 01 2025 *)
If p = 3, then M_3 = 7 and a(1) = 2^(2*3)*3*7^2 = 9408, with spectral basis {63^2, 56^2, 48^2}, and spectral sum equal to 1*9408 + 1 = 9409. However, {63^2, 56^2, 48^2} is also the spectral basis of A330836(1) = 4704, with spectral sum equal to 2*4704+1.
a := proc(n::posint) local p, m; p:=NumberTheory[IthMersenne](n+1); m:=2^p-1; return 2^(2*p)*3*m^2; end:
f[p_] := 2^(2p)*3*(2^p - 1)^2; f /@ MersennePrimeExponent /@ Range[2, 9] (* Amiram Eldar, Jan 17 2020 *)
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