

A164340


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


1



1, 2, 3, 4, 5, 9, 7, 16, 27, 32, 11, 512, 13, 128, 243, 65536, 17, 134217728, 19, 4294967296, 2187, 2048, 23
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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 largest possible value of this tower, considering all permutations q.
a(24) = 2^(2^(3^2)) is 155 digits and too long to display.


LINKS

Table of n, a(n) for n=1..23.


EXAMPLE

The primes dividing 12 are (with repetition): 2, 2, 3. There are three distinct exponent towers that can be constructed with these primes: 2^(2^3) = 256, 2^(3^2) = 512, and 3^(2^2) = 81. a(12) = the largest of these, which is 512.


CROSSREFS

Cf. A164339.
Sequence in context: A327415 A072501 A092975 * A046021 A319023 A335910
Adjacent sequences: A164337 A164338 A164339 * A164341 A164342 A164343


KEYWORD

nonn


AUTHOR

Leroy Quet, Aug 13 2009


EXTENSIONS

Extended by Ray Chandler, Mar 16 2010


STATUS

approved



