27637 is a product of two 4k+1 primes and so it can be expressed as a sum of two squares in two ways viz. 9^2 + 166^2 and 114^+ 121^2.
27637 is a member of OEIS A340157: numbers m such that numbers m, m + 1, m + 2 and m + 3 have k, 2k, 3k and 4k divisors respectively, here 4, 8, 12, 16.
The sequence can be generated as follows:
INPUT
L=[]
for n in [1..40000]:
a=sigma(n,0)
b=sigma(n+1,0)
c=sigma(n+2,0)
d=sigma(n+3,0)
if b/a==2 and (c/a==3 and d/a==4):
L.append(n)
if n==27637:
print(sigma(n,0),sigma(n+1,0),sigma(n+2,0),sigma(n+3,0))
print(L)
OUTPUT
4 8 12 16
[421, 3013, 5029, 5223, 5245, 5893, 6487, 10533, 11911, 14677, 17173, 23077, 23573, 24613, 25141, 25213, 27637, 27973, 28357, 30661, 32407, 34117, 37477, 38282, 39751]
27637 is a cyclic and Duffinian number.
27637 has a sum of proper divisors that is prime (983) and thus its aliquot sequence has three steps:
- 27637 --> 983 --> 1 --> 0
27637 has a product of digits of 1764 and
- 27637 + 1764 = 29401 which is a prime number
- 27637 - 1764 = 25873 which is a prime number
27637 can be rendered as a digit equation as follows:
-2 + 7 = -6 / 3 + 7