## Archive for March 21, 2011

### What is Your Favorite Number?

The WordPress Post-A-Week Challenge sends me a daily topic idea to consider for blog posts. Often, the prompts are not appropriate for a math jokes blog. For instance, some recent prompts have been:

- Grab the nearest book (or website) to you right now. Jump to paragraph 3, second sentence. Write it in a post.
- How do you find your muse?
- If you could bring one fictional character to life for a day, who would you choose?

But today’s prompt landed in my wheelhouse:

What is your favorite number, and why?

When Art Benjamin appeared on the Colbert Report, he said that 2,520 was his favorite number when he was a kid. When Stephen Colbert asked him why, he replied, “It was the smallest number that was divisible by all the numbers from 1 through 10.”

Tonight, I asked my twin sons Alex and Eli what their favorite numbers are.

Eli: 5, 15, 55, because my favorite number is really 5, but 15 and 55 are triangular numbers that have 5’s in them.

Alex: 21, because my favorite numbers used to be 1 and 2, and because it’s the number of cards you deal when we play Uno (3 players, 7 cards each).

My favorite number is 153, for lots of reasons:

- It is the smallest non-trivial Armstrong (or narcissistic) number — that is, it is an
*n*‑digit number that is equal to the sum of the*n*th powers of its digits: 1^{3}+ 5^{3}+ 3^{3}= 153. - Its prime factors are 3 and 17, and my birthday is 3/17.
- It is a triangular number. (Consequently, it’s the sum of 1 + 2 + 3 + … + 17.) As 351 is also a triangular number, 153 is also a reversible triangular number.
- It is the sum of the first five factorials: 1! + 2! + 3! + 4! + 5! = 153.
- The sum of its digits is 9, and the sum of its proper divisors is 9
^{2}. - It is one of only six known truncated triangular numbers, which means that 1, 15 and 153 are all triangular numbers.

Mathematician John Baez claims that his favorite numbers are 5, 8, and 24.

Got a favorite number? Share it, as well as the reason it’s your favorite, in the comments.