WOLFRAM|DEMONSTRATIONS PROJECT

Odd and Even Values of Divisor Functions

k

1

f(n)

σ

0

(n)

n -

σ

0

(n)

σ

k

(n)

σ

k

(n) - n

n

plot values

all

only odd

only even

plot type

list plot

polar plot

log plot

framed

The divisor function

σ

k

(n)

is the sum of the

th

k

powers of the divisors of

n

, where

k

and

n

are positive integers;

σ

0

(n)=d(n)

is the number of divisors of

n

and

σ

1

(n)=σ(n)

is the sum of the divisors of

n

.

σ

k

(n)-n

, the sum of the proper divisors of

n

, is called the aliquot sum of

n

.