[Verse 1]
When numbers hide their secrets deep inside
Tau function counts the doors that open wide
Every divisor standing in a row
How many factors does your number show?
[Verse 2]
Sigma takes a different approach tonight
Adds up divisors, sums them left to right
Not just the count but total weight they bear
Mathematical treasure buried there
[Chorus]
Tau counts the pieces, sigma adds them whole
Möbius dances with a different goal
One if it's lonely, zero if there's squares
Negative one when distinct primes declare
Functions that unlock the patterns underneath
Mathematical tools beyond belief
[Verse 3]
Möbius plays by rules that twist and turn
At one it starts, then watch the bridges burn
Product of distinct primes gets minus one raised high
But squared factors make the function die
[Verse 4]
Six has divisors one, two, three, and six
Tau of six equals four, that's how it clicks
Sigma sums them up to twelve complete
While Möbius gives us one, the cycle sweet
[Chorus]
Tau counts the pieces, sigma adds them whole
Möbius dances with a different goal
One if it's lonely, zero if there's squares
Negative one when distinct primes declare
Functions that unlock the patterns underneath
Mathematical tools beyond belief
[Bridge]
When four appears with two times two inside
Möbius turns to zero, cannot hide
Squared prime factors kill the dancing flow
But tau and sigma still have room to grow
[Outro]
Three functions weaving through the number maze
Counting, summing, switching minus ways
Tau and sigma, Möbius combined
Essential tools for mathematical minds