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A300217
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Numbers k such that tau(phi(k)) is a prime.
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1
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3, 4, 5, 6, 8, 10, 12, 17, 32, 34, 40, 48, 60, 85, 128, 136, 160, 170, 192, 204, 240, 1285, 2048, 2056, 2176, 2560, 2570, 2720, 3072, 3084, 3264, 3840, 4080, 4369, 8192, 8224, 8704, 8738, 10240, 10280, 10880, 12288, 12336, 13056, 15360, 15420, 16320, 65537
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OFFSET
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1,1
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COMMENTS
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Numbers k such that A000010(k) = 2^(p-1) where p is prime.
Numbers of the form 2^m*Product_{i=1..k} (2^(2^(e_i))+1) where 2^(2^(e_i)+1) are distinct Fermat primes (A019434) and m + 1 + Sum_i 2^(e_i) is prime. In particular the prime terms are A249759.
(End)
According to a comment in A009087, if the sum of divisors is prime, then the number of divisors is also prime. - Michael B. Porter, Mar 23 2018
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LINKS
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EXAMPLE
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17 is a term because phi(17) = 16, tau(16) = 5 (prime).
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MAPLE
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select(isprime @ numtheory:-tau @ numtheory:-phi, [$1..10^5]); # Robert Israel, Mar 18 2018
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MATHEMATICA
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Select[Range[2^16 + 1], PrimeQ@ DivisorSigma[0, EulerPhi@ #] &] (* Michael De Vlieger, Mar 01 2018 *)
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PROG
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(Magma) [n: n in[1..10^6] | IsPrime(NumberOfDivisors(EulerPhi(n)))]
(PARI) isok(k) = isprime(numdiv(eulerphi(k))); \\ Altug Alkan, Mar 04 2018
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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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