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A335120
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The prime terms of A225563.
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0
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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