27306 is a product of 2, a 4k+3 prime raised to an even power and two 4k+1 primes and so it can be expressed as a sum of two squares in two different ways viz. 9^2+165^2 and 45^2+159^2.

27306 is a member of OEIS A140359: a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) with a(0)=a(1)=1 and a(3)=6. The sequence can be generated as follows:

INPUT

a,b,c=1,1,6

L=[a,b,c]

for n in [1..14]:

  d=2*c+b-2*a

  L.append(d)

  a,b,c=b,c,d

print(L)

OUTPUT

[1, 1, 6, 11, 26, 51, 106, 211, 426, 851, 1706, 3411, 6826, 13651, 27306, 54611, 109226]

The OEIS comments note that this sequence is identical to a(n) = a(n-1) + 2*a(n-2) +3. It also notes that a(n+1) - a(n) = 5*A001045(n) where this OEIS sequence is the Jacobsthal numbers.

27306 is a Harshad number since it is a multiple of its sum of digits (18).

27306 is a practical number because each smaller number is the sum of distinct divisors of 27306. 

27306 is an abundant, Zumkeller and pseudoperfect number.