Value of $\mu (20)+σ(20) $ is (where $\mu(n)$ is the Mobius function and $σ(n)$ is the sum of all positive divisors of n)

42

The correct answer is Option (4) → 42

Mobius function, $\mu(n)$ is defined as:

$\mu(n)=0$, if n has a squared price factor

$\mu(n)=1$, if n is square-free with even no. of primes

$\mu(n)-1$, if n is square free, with odd no. of prime factors

For $n=20$,

$20 = 2^2 \times 5$

$μ(20)=0$

Now, the function $σ(n)$ is the sum of all positive divisors of $n$.

Divisors of 20: 1, 2, 4, 5, 10, 20

$σ(20)=1+2+4+5+10+20=42$

$μ(20)+σ(20)=0+42=42$