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A280256
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Numbers k such that tau(k^k) is a prime.
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3
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2, 9, 6561, 25937424601, 1853020188851841, 58149737003040059690390169, 54116956037952111668959660849, 2787593149816327892691964784081045188247552, 2465034704958067503996131453373943813074726512397600969
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OFFSET
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1,1
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COMMENTS
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tau(k) is the number of positive divisors of k (A000005).
Corresponding values of primes: 3, 19, 52489, ...
All the terms are prime powers.
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LINKS
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EXAMPLE
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tau(9^9) = tau(387420489) = 19 (prime).
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MATHEMATICA
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mx = 10^200; Union@ Flatten@ Reap[ Sow[2^ Select[ Range@ Log2[mx], PrimeQ[1 + # 2^#] &]]; Do[ If[ PrimeQ[1 + q p^q], Sow[p^q]], {p, Prime@ Range@ PrimePi@ 34}, {q, 2, Log[p, mx], 2}]; Do[ Sow@ (Select[ Prime@ Range[2, PrimePi[ mx^(1/e)]], PrimeQ[1 + e #^e] &]^e), {e, 34, Floor@Log[31, mx], 2}]][[2, 1]] (* all the 231 terms < 10^200, Giovanni Resta, Mar 07 2017 *)
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PROG
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(Magma) [n: n in [1..500] | IsPrime(NumberOfDivisors(n^n))]
(PARI) isok(n) = isprime(numdiv(n^n)); \\ Michel Marcus, Mar 07 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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