27731 is a member of OEIS A000124: central polygonal numbers (Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts, here n=235. In short, 27731 is a pancake number.

Here is an excerpt from the OEIS comments:

"The first line cuts the pancake into two pieces. For n > 1, the n-th line crosses every earlier line (avoids parallelism) and also avoids every previous line intersection, thus increasing the number of pieces by n. For 16 lines, for example, the number of pieces is 2 + 2 + 3 + 4 + 5 + ... + 16 = 137. These are the triangular numbers plus 1".

27731 is a de Polignac number because none of the positive numbers 27731 - 2^k is a prime.

27731 is the last in a run of FOUR consecutive positive negabinary-Niven numbers. The first number was 27728.

27731 is a cyclic & Duffinian number.

27731 forms a pair with 27730 with both numbers having the property that the number plus its sum of digits is prime. Specifically:

27730 + 19 = 27749 (prime)

27731 +21 = 27751 (prime)

27731 has a totient (25200) that is a multiple of a primorial: The totient is 25200 = 2^4 * 3^2 * 5^2 * 7 = 210 * 2^3 * 3 * 5.

27731 can be rendered as a digit equation as follows:

2 + 7 / 7 = 3 * 1