|
%I #10 Mar 11 2014 01:32:45
%S 1,2,3,4,5,8,7,16,27,25,11,81,13,49,125,65536,17,6561,19,625,343,121,
%T 23,43046721,3125,169,7625597484987,2401,29,390625,31
%N Write down the primes dividing n (with repetition) in an exponent tower (see comment). a(n) = the smallest possible value of such a tower.
%C Clarification of definition: If p^j = the largest power of the prime p to divide n, then write down the prime p a total of j times. Do this for all primes dividing n. Next, take a permutation q = (q(1), q(2),...q(r)) (r = sum of the exponents in the prime-factorization of n) of all these primes, and write them in a exponent tower like this: q(1)^(q(2)^(q(3)^(...^q(r)))). a(n) = the smallest possible value of this tower, considering all permutations q.
%C a(32) = 2^2^2^2^2 is 19729 digits and too long to display.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_factor">Prime factor</a>
%e The prime factorization of 12 is 2*2*3. The exponent tower permutations of these non-distinct prime factors are: 2^(2^3) = 256, 2^(3^2) = 512, and 3^(2^2) = 81. a(12) = the smallest of these, which is 81.
%Y Cf. A164340.
%K nonn
%O 1,2
%A _Leroy Quet_, Aug 13 2009
%E Extended by _Ray Chandler_, Mar 16 2010
%E Example edited by _Vincent Murphy_, Oct 17 2012
|
