[seqfan] Re: A071390

[Don Reble]

> A071390 is "Least number m such that sigma(m) - phi(m) = n,
> or 0 if no such m exists."

> The Mathematica code computes sigma(m) - phi(m) for m up to 1000, ...
> it would be nice to have a theoretical result for how far we
> need to search in general.

For prime p, sigma(p)-phi(p) = 2; s(p^2)-p(p^2) = 2p+1; s(8)-p(8) = 11.
For other numbers, sigma(n)-phi(n) > 4*sqrt(n).
After checking n=2, n=11, and isPrime((n-1)/2), search to (n/4)^2.

-- 
Don Reble  djr at nk.ca