27562 is a product of 2 and a 4k+1 prime and can therefore be expressed as a sum of two squares in one way only viz. 151^2 + 69^2.

27562 is a Catch-22 number in which the digit 2 occurs in the first and last positions and in which the sum of the digits is 22. The sequence can be generated as follows:

INPUT

L=[]

for n in [22..40000]:

  D=n.digits()

  if sum(D)==22:

    OK=1

    if D[0]==2 and D[len(D)-1]==2:

      for i in range(1,len(D)-1):

        if D[i]==2:

          OK=0

          break

      if OK==1:

        L.append(n)

print(L)

print(len(L))

OUTPUT

[2992, 20992, 21892, 21982, 23692, 23782, 23872, 23962, 24592, 24682, 24772, 24862, 24952, 25492, 25582, 25672, 25762, 25852, 25942, 26392, 26482, 26572, 26662, 26752, 26842, 26932, 27382, 27472, 27562, 27652, 27742, 27832, 28192, 28372, 28462, 28552, 28642, 28732, 28912, 29092, 29182, 29362, 29452, 29542, 29632, 29812, 29902]

47

27562 is a Smith, hoax, untouchable number.

27562 is a powerful number because it can be written as 2^4 + 7^2 + 5^6 + 6^5 + 2^12 .

27562 can be rendered as a digital equation as follows:

-2 - 7 + 5 + 6 = 2