
COMMENTS

a(10) = 10^273  273^10 is too large to include.
a(16) = 1 because primes of the form (16^k  k^16) do not exist, since 16^k  k^16 = (4^k  k^4)(4^k + k^4).
The corresponding numbers k such that a(n) = (n^k  k^n) are listed in A128355(n) = {0,5,4,0,14,7,20,11,10,273,14,13,38,89,68,0,...}, where k = 0 corresponds for definite a(n) = 1. Currently a(n) is not known for n = {17,18,22,25,26,27,28,...}.


EXAMPLE

a(1) = 1 because (1^k  k^1) = (1  k) < 0 for k > 1.
a(2) = 7 because 2^5  5^2 = 7 is prime, but (2^k  k^2) is not prime for 1 < k < 5, (2^2  2^2) = 0, (2^3  3^2) = 1, (2^4  4^2) = 0.
a(4) = 1 because prime of the form (4^k  k^4) does not exist, 4^k  k^4 = (2^k  k^2)(2^k + k^2).
a(12) = 83695120256591 = 12^13  13^12 = A024152[ A122003(2) ].
