JFL-Quiz on Tau and Sigma Functions

What does the tau function (τ(n)) represent?

• Sum of all prime factors of n

• Number of positive divisors of n

• Product of all divisors of n

• Largest divisor of n

Which of the following is true about the sigma function (σ(n))?

• It counts the number of prime numbers less than n

• It gives the number of divisors of n

• It gives the sum of all positive divisors of n

• It gives the average of the factors of n

If n is a prime number, how many positive divisors does it have?

• 0

• 1

• 2

• Infinite

Which is a correct interpretation of τ(12)?

• τ(12) = 12

• τ(12) = 28

• τ(12) = 6

• τ(12) = 3

Given that σ(12) = 28, what does this mean?

• The number of divisors of 12 is 28

• The product of the divisors is 28

• The sum of the divisors of 12 is 28

• The largest divisor is 28

What is τ(7)?

• 1

• 2

• 3

• 7

What is σ(5²)?

• 6

• 25

• 31

• 15

What is τ(9)?

• 2

• 3

• 4

• 6

Find σ(16).

• 31

• 36

• 20

• 25

Find τ(84).

• 10

• 12

• 8

• 14