27325 is a product of two 4k+1 prime factors, one raised to the power of 2, and so it can be expressed as the sum of two squares in three different ways viz. 10^2+165^2 and 91^2+138^2 and 107^2+126^2.

27325 is the greater of a pair of adjacent composite numbers such that both are only one step away from their home primes (here 551093). See Bespoken for Sequences entry.

27325 is a happy and lucky number. Hence it can be termed a happy go lucky number. See blog post Asymptotic Density of Happy Go Lucky Numbers.

27325 is a Duffinian number meaning that it has no factors in common with its sum of divisors 33914 = 2 * 31 * 547.