27338 is a product of 2 and a 4k+1 prime so it can be expressed as a sum of two squares in one way only viz. 143^2 + 83^2.

27338 is a semiprime n such n-1 is prime and n+1 and n+2 have 3 and 4 factors with multiplicity, thus part of a 1-2-3-4 factor progression. See entry for 27337. The initial semiprimes are:

194, 422, 662, 1094, 1658, 2138, 2342, 2594, 6218, 7058, 8102, 9818, 12422, 12854, 15122, 16034, 16418, 17258, 17882, 19814, 20642, 21818, 25034, 25658, 27338, 28922, 30662, 31082, 31322, 31334, 32378, 35522, 36458, 38282