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.
%I A335120 #18 Mar 31 2022 04:26:17
%S A335120 3,5,7,11,13,17,31,41,61,97,103,137,193,241,257,409,641,769,1021,1361,
%T A335120 1543,5441,6529,7681,8161,12289,15361,17477,26113,30841,40961,43691,
%U A335120 61441,61681,65537,82241,87041,98689,131071,163841,174761,328961,417793,557057,786433
%N A335120 The prime terms of A225563.
%C A335120 Apparently, the prime terms of A225563 are relatively rare. For example, of the first 10^4 terms of A225563, only 23 are primes.
%C A335120 Alternatively, odd primes p such that phi(phi(p)), the number of primitive roots modulo p, is a power of two. Primes such that all odd prime divisors of p-1 are Fermat primes. - _Paul Vanderveen_, Mar 29 2022
%t A335120 totQ[n_] := PrimeQ[n] && Module[{it = Most@FixedPointList[EulerPhi, n], sum, x}, sum = Plus @@ it; If[OddQ[sum], False, CoefficientList[Product[1 + x^i, {i, it}], x][[1 +sum/2]] > 0]]; Select[Range[10^3], totQ]
%Y A335120 Cf. A225563.
%K A335120 nonn
%O A335120 1,1
%A A335120 _Amiram Eldar_, May 24 2020