27364 is product of a power of 2 and a 4k+1 prime, thus it can be expressed as a sum of two squares in one way only viz. 160^2 + 42^2.

27364 is a member of OEIS A047827: becomes prime after exactly 8 iterations of f(x) = sum of prime factors of x. There are only 18 such composite numbers in the range up to 40,000. The sequence can be generated as follows (permalink):

INPUT

def decide(n):

  total=0

  number=n

  count=0

  while is_prime(total) == 0:

    F=prime_factors(n)

    total=sum(F)

    n=total 

    count+=1

  return number,count

L=[]

for n in [4..40000]:

  if decide(n) [1]==8:

    L.append(decide(n) [0])

print(L)

print(len(L))

OUTPUT

[13682, 18002, 19137, 22934, 24014, 24787, 27364, 27849, 30062, 30993, 32577, 33477, 35410, 35798, 36004, 36398, 36706, 39206]

18

In the case of 27364, the progression is as follows (permalink):

  number   factorisation   prime factors   sopf

  27364    2^2 * 6841      [2, 6841]       6843
  6843     3 * 2281        [3, 2281]       2284
  2284     2^2 * 571       [2, 571]        573
  573      3 * 191         [3, 191]        194
  194      2 * 97          [2, 97]         99
  99       3^2 * 11        [3, 11]         14
  14       2 * 7           [2, 7]          9
  9        3^2             [3]             3

27364 is an interprime number because it is at equal distance from previous prime (27361) and next prime (27367).

27364 is a d-powerful number because it can be written as 2^11 + 7^5 + 3^6 + 6^5 + 4 .

27364 stabilises after about 135 generations to a block and a glider under Conway's Game of Life rules.