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Zanzabum
4 years ago
7

The sum of the divisors function \sigma (n) is not a multiplicative function. True False

Mathematics
1 answer:
maks197457 [2]4 years ago
6 0

Answer:

True.

Step-by-step explanation:

If a function is multiplicative then it hold following properties

1.f(1)=1

2.\f(a\cdot b)=f(a)\cdot f(b) hold for all a and b when  even a and b are not co-prime.

Let \sigma(n) is a function of  sum of divisor of n

\sigma (n)=Sum of divisor of n

If n=1 then

\sigma (1)=1

It is satisfied first property.

Suppose n=9

Then divisor of 9=1,3,9

Sum of divisor=1+3+9=13

Divisor of 3=1,3

Sum of divisors of 3=1+3=4

\sigma (9)=13

\sigma (3)\cdot \sigma(3)=4\cdot 4=16

Hence, \sigma (a\cdot b)\neq \sigma(a)\cdot \sigma(b)

Therefore, \sigma(n) is not a multiplicative function.

Hence, given statement is true.

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