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, 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

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

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 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

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