A072507

[Dean Hickerson]

Mostly to Franklin T. Adams-Watters:

> The next question is, what is the length, for a given n, of the longest 
> sequence of integers with exactly n divisors?
...
> 6 4 or 5
...
> If the case n=6 can be resolved, I will go ahead and submit the sequence.

The longest sequence has length 5:

    10093613546512321 = 7^2 205992113194129
    10093613546512322 = 2 71040881^2
    10093613546512323 = 3^2 1121512616279147
    10093613546512324 = 2^2 2523403386628081
    10093613546512325 = 5^2 403744541860493

I don't know if this is the smallest example; I only looked for ones in which
the last 4 numbers have the forms  2 p^2,  3^2 q,  2^2 r,  and  5^2 s,  with
primes p, q, r, and s.

Dean Hickerson
dean at math.ucdavis.edu