27506 is a product of 2 and two 4k+2 primes and therefore it can be expressed as a sum of two squares in two different ways viz. 59^2+155^2 and 109^2+125^2.

27506 is a member of OEIS A063434: integers n > 10577 such that the 'Reverse and Add!' trajectory of n joins the trajectory of 10577. As far as is known, numbers like 20577 and thus 27506, do not produce palindromes under the reverse and add algorithm.

The initial members are:

11567, 12557, 13547, 14537, 15527, 16517, 17507, 20576, 21566, 22556, 23546, 24536, 25526, 26516, 27506, 30575, 31565, 32555, 33545, 34535, 35525, 36515, 37505, 40574, 

27506 is a sphenic number.

27506 can be rendered as a digit equation as follows:

-2 + 7 - 5 = 0 * 6