A225563 -id:A225563 - cp's OEIS frontend

A335120 The prime terms of A225563.

3, 5, 7, 11, 13, 17, 31, 41, 61, 97, 103, 137, 193, 241, 257, 409, 641, 769, 1021, 1361, 1543, 5441, 6529, 7681, 8161, 12289, 15361, 17477, 26113, 30841, 40961, 43691, 61441, 61681, 65537, 82241, 87041, 98689, 131071, 163841, 174761, 328961, 417793, 557057, 786433

Offset: 1

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Amiram Eldar, May 24 2020

nonn

Apparently, the prime terms of A225563 are relatively rare. For example, of the first 10^4 terms of A225563, only 23 are primes.

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

Cf. A225563.

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]

cp's OEIS Frontend

A335120 The prime terms of A225563.

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