A073087(5)

[Mitchell Harris]

On Wed, 14 Sep 2005, Lambert Klasen wrote:

>ID Number: A073087
>URL:       http://www.research.att.com/projects/OEIS?Anum=A073087
>Sequence:  1,6,30,210
>Name:      Least k such that sigma(k^k)>=n*k^k.

...
>and the next term in the sequence a(5) is most likely 30030.

a(5) is certainly 30030...

>but i cannot compute a(5) due to lack of memory.
>using PARI, it needs more then 1GB of memory which i unfortunately
>do not possess.
>
>anyone help ?

Instead of computing k^k and then sigma of that (for large k), just use 
the identity 

  sigma(k^k) = prod (p^(k r + 1) - 1)/(p - 1) 

(where the product is over all prime power factors p^r). This speeds 
things up enormously for a(5) (using Mathematica). I am not so patient for 
a(6) though...

Mitch