n through n+7 have same d() / A049053

[Jud McCranie]

At 04:16 AM 11/2/2004, Ralf Stephan wrote:
>Hello,
>A049053 gives all numbers n where n,n+1,...,n+6 have the same number
>of divisors. Allan Swett gave a counterexample to my conjecture that
>n is 5 mod 16 while searching for solutions to the problem with n...n+7.
>
>He asks:
> > I was hoping to find 8 consecutive having same d()... I
> > didn't spot evidence of this so far... do you know if this is impossible?

It is not impossible, but it gets a lot harder for 8 in a row because you 
have one number that is divisible by 8 and one that is divisible by 4 but 
not divisible by 8.  There are solutions with 9 in a row, I'm pretty sure 
they are in Unsolved Problems in Number Theory.