Fun math facts about 2023

(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.

2023 is the sum of the squares of the first five prime numbers (2^2 + 3^2 + 5^2 + 7^2 + 11^2 = 2023).

2023 is a deficient number, meaning the sum of its proper divisors (1, 7, 11, 41, 77, 121, 187, 287) is less than 2023.

2023 is the hypotenuse of a Pythagorean triple (1875, 1750, 2023).

2023 is the sum of the first 25 positive integers (1 + 2 + 3 + ... + 25 = 2023) AND

2023 is the sum of the first 50 odd integers (1 + 3 + 5 + ... + 99 = 2023).

2023 is the 500th number in the Fibonacci sequence.