27585 is a product of a 4k+3 prime raised to an even power (2) and two 4k+1 primes. Thus is can be expressed as a sum of two squares in two different ways viz. 48^2 + 159^2 and 57^2 + 156^2.

27585 is a member of OEIS A063871: trajectory of 3 under map n->7n-1 if n odd, n->n/2 if n even. The sequence can be generated as follows (permalink):

INPUT

start=3

number=start

L=[start]

for n in [1..40]:

  if is_odd(number):

    number=number*7-1

  else:

    number=number/2

  L.append(number)

print(L)

list_plot(L,plotjoined=True)

OUTPUT

[3, 20, 10, 5, 34, 17, 118, 59, 412, 206, 103, 720, 360, 180, 90, 45, 314, 157, 1098, 549, 3842, 1921, 13446, 6723, 47060, 23530, 11765, 82354, 41177, 288238, 144119, 1008832, 504416, 252208, 126104, 63052, 31526, 15763, 110340, 55170, 27585]

27585 is a happy, Curzon, inconsummate and lucky number.

27585 is digitally balanced in base 4 (12233001) meaning it has all possible digits an equal number of times.

27585 can be rendered as a digit equation as follows:

2 | (7 - 5 + 8) = 5