Sum Of Lesser Divisors

[Leroy Quet]

If we let s(m) =

sum{k|m, 1<=k<=sqrt(m)} k^2,

then what is the sequence of m's where

s(m) >= sum{k|m} k  = sigma(m) ?

m = 1 and m = 900 are included. 



A related question:

What is the *highest* real x such that

sum{k|m, 1<=k<=sqrt(m)}  k^x

is < sum{k|m} k  = sigma(m)

for EVERY m >= 2 ?

thanks,
Leroy Quet