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, 2, 3, 4, 5, 9, 7, 16, 27, 32, 11, 512, 13, 128, 243, 65536, 17, 134217728, 19, 4294967296, 2187, 2048, 23

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 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