OFFSET
1,2
COMMENTS
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.
a(32) = 2^2^2^2^2 is 19729 digits and too long to display.
LINKS
Wikipedia, Prime factor
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Aug 13 2009
EXTENSIONS
Extended by Ray Chandler, Mar 16 2010
Example edited by Vincent Murphy, Oct 17 2012
STATUS
approved