27555 is a member of OEIS A341780: starts of runs of three consecutive anti-tau numbers (see OEIS A046642). See blog posts titled Anti-tau Numbers and Tau Numbers. The sequence can be generated as follows:

INPUT

L=[]

for n in [1..40000]:

  if gcd(n,len(divisors(n)))==1:

    L.append(n)

M=[]

for m in L:

  if m+1 in L and m+2 in L:

    M.append(m)

print(M)

print(len(M))

OUTPUT

[3, 15, 195, 255, 483, 783, 1023, 1155, 1295, 1443, 1599, 2703, 3363, 4623, 4899, 5183, 6399, 6723, 7395, 7743, 8463, 8835, 10815, 11235, 11663, 12099, 12543, 15375, 16383, 16899, 17955, 18495, 20163, 24963, 25599, 26895, 27555, 31683, 33855, 35343, 36099, 37635, 38415]

43

27555 is a Cunningham number because it is equal to 166^2-1.

27555 does NOT reach a home prime after 50 iterations.

27555 is a composite number with all its digits prime.

27555 is a a Smith number, since the sum of its digits (24) coincides with the sum of the digits of its prime factors. Since it is squarefree, it is also a hoax number.

27555 can be rendered as a digit equation as follows:

-2 + 7 = 5 + 5 - 5