slightlyexcessivenumbers

Slightly Excessive Numbers

No slightly excessive numbers exist (a slightly excessive number, n, is one for which sigma(n) would = 2n+1)

Proof:

Suppose sigma(n) = 2n+1

sigma(pn) == 0 [mod 2] [hcf (p,n)=1]

Let p->99999... [Euclid]

sigma(pn)/p = 2n+1

But L.H.S. == 0 [mod 2] , while R.H.S. == 1 [mod 2]