Template:Sequence of the Day for August 12

Intended for: August 12, 2011

Timetable

• First draft entered by Alonso del Arte on May 12, 2011 ✓
• Draft reviewed by Alonso del Arte on August 10, 2011 ✓
• Draft to be approved by July 12, 2011

Yesterday's SOTD * Tomorrow's SOTD

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A048855:

φ (n!)

, the totient function of the factorial of

n

.

{ ..., 1, 2, 8, 32, 192, 1152, 9216, ... }

These are the numbers of integers less than

n!

that are coprime to said factorial (I choose to start the listing here with

a2

). There’s also a recurrence relation to explain these, which was found by Enoch Haga and goes by the offset shown here:

a1 = 1

, then, if

n

is prime,

an = (n  −  1) an  − 1

, otherwise

an = n an  − 1

. Also note how small these numbers are compared to the factorials. For example, 20! = 2432902008176640000, while

φ (20!)

is just 416084687585280000, less than a fifth of 20!.