27721 is a member of OEIS A137199: a(n)=a(n-1)+3a(n-2)+a(n-3) where a(0)=a(1)=a(2)=1. The initial terms are:

1, 1, 1, 5, 9, 25, 57, 141, 337, 817, 1969, 4757, 11481, 27721.

27721 is a 4-Lehmer number meaning that euler_phi(27721) = 26244 divides (27721 - 1)^4. See blog post Lehmer Numbers. In this case the quotient is 22497946240000.

27721 is a cyclic and Duffinian number.

27721 is a Harshad number since it is a multiple of its sum of digits (19), and also a Moran number because the ratio is a prime number: 1459 = 27721 / (2 + 7 + 7 + 2 + 1).

27721 is a centered 44-gonal number.

27721 can be rendered as a digit equation as follows:

2 - 7 / 7 = 2 - 1