1. Sums of divisors

Let integer n be factorized as

n = p₁^e₁ * p₂^e₂ * ... * p_k^e_k

then the sum of divisors of n is represented as the following formula,

σ(n) = a₁ * a₂ * ... * a_k

where

ak =	pkek+1 - 1
	------------
	pk - 1

Especially,

pkek+1 - 1	= pkek + ... + pk2 + pk + 1
------------
pk - 1

so if n=p^e then

σ(n) = p^e + ... + p² + p + 1.

When we compute the sum of divisors during factorization of n,
this formula is more easy to handle. The algorithm is following,

1. Let w=1 (σ(n) is stored in w).
2. p=prmdiv(n)
If p|n then

w = w*p+1
n = n/p

3. If p does not divide n then terminate.
The value p^e + ... + p² + p + 1 is stored in w.
4. goto 2.

The value of σ(n) where n = p₁^e₁ * p₂^e₂ * ... * p_k^e_k
is calculated by the following procedure.

1. Let s=1 (σ(n) is stored in s).
2. Let p be the smallest divisor of n.
If p=1 then terminate.
3. repeat 1. through 4. of above procedure.
If the condition 3. is held, let

s = s * w.

4. goto 2.

The program is following.

10   fnSigma(N)
20   local S,W,P
30   S=1
40   W=1:P=prmdiv(N)
50   if N@P=0 then W=W*P+1:N=N\P:goto 50 else S=S*W
60   if N>1 then 40 else return(S)