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A280256
Numbers k such that tau(k^k) is a prime.
3
2, 9, 6561, 25937424601, 1853020188851841, 58149737003040059690390169, 54116956037952111668959660849, 2787593149816327892691964784081045188247552, 2465034704958067503996131453373943813074726512397600969
OFFSET
1,1
COMMENTS
tau(k) is the number of positive divisors of k (A000005).
Numbers k such that A000005(A000312(k)) = A062319(k) is a prime.
Corresponding values of primes: 3, 19, 52489, ...
All the terms are prime powers.
LINKS
EXAMPLE
tau(9^9) = tau(387420489) = 19 (prime).
MATHEMATICA
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 *)
PROG
(Magma) [n: n in [1..500] | IsPrime(NumberOfDivisors(n^n))]
(PARI) isok(n) = isprime(numdiv(n^n)); \\ Michel Marcus, Mar 07 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Mar 07 2017
EXTENSIONS
a(4)-a(9) from Giovanni Resta, Mar 07 2017
STATUS
approved