Question

when n=14,206 & 957
show that sigma(n)=sigma(n+1)

Answer 1

\[\sigma(14)=\sigma(2*7)=24=\sigma(3*5)=\sigma(15)\]

Answer 2

is it 2*7 because that is the prime factorization?
then i assume you would \[2^2-1/2-1*7^2-1/7-1 \] which is 8? not 24

Answer 3

\(\sigma(14) = \sigma(2) \sigma(7) = (1+2)(1+7) = 24\)

Answer 4

oh okay so you take sigma of each individual prime factor

Answer 5

and how does that equal to (3*5)?

Answer 6

yes cuz \(\sigma\) is a multiplicative function :
\(\sigma(ab) = \sigma(a) \sigma(b)\)

Answer 7

im sorry one more question how is that equal to 3*5?

Answer 8

\(\sigma(15) = \sigma(3) \sigma(5) = (1+3)(1+5) = 24\)

Answer 9

okay got it thanks!