

A164339


Write down the primes dividing n (with repetition) in an exponent tower (see comment). a(n) = the smallest possible value of such a tower.


1



1, 2, 3, 4, 5, 8, 7, 16, 27, 25, 11, 81, 13, 49, 125, 65536, 17, 6561, 19, 625, 343, 121, 23, 43046721, 3125, 169, 7625597484987, 2401, 29, 390625, 31
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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 primefactorization 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

Table of n, a(n) for n=1..31.
Wikipedia, Prime factor


EXAMPLE

The prime factorization of 12 is 2*2*3. The exponent tower permutations of these nondistinct 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

Cf. A164340.
Sequence in context: A298882 A086931 A243405 * A275465 A185198 A297338
Adjacent sequences: A164336 A164337 A164338 * A164340 A164341 A164342


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



