(These are stolen from @joshuacooper@mathstodon.xyz, who found them by looking for 2023 in OEIS.)
It's the number of tilings of a 4×4 square with right triominoes and 1×1 tiles.
It's the sum over all 4-tuples (a,b,c,d) of divisors of 18 of the quantity gcd(a,b,c,d).
It's the number of connected (unlabeled) graphs on 9 vertices that occur as induced subgraphs of a Hamming graph (=Cartesian product of paths).
(A few more from my own OEIS-mining.)
2023 = 45^2 - 2. (Not very exciting, but surely no worse than 2^11 - 5^2.)
The number n=28322 has the (quite unusual; it's 16th-smallest) property that n^2 is a multiple of the sum of all distinct prime divisors of n^2+1. The quotient is 2023^2.
2023 is the remainder on dividing 7^7 by 7!.
Let A(n) be the average of all primes dividing n. Then 2023 is the second-smallest positive integer n for which A(n) and A(n+1) are equal. (The smallest is 459.)
2023 = (2+0+2+3)(2^2+0^2+2^2+3^2)^2; 2023 is the smallest number other than 1 for which this happens.
Maybe that's not fun enough? Try this:
Or better yet:
We can scientifically quantify how fun a math fact is, so we can rest assured that this is the funnest fact about 2023 ever discovered.
But if it's not to your liking:
Happy New Year!