4165 has 12 divisors (see below), whose sum is σ = 6156. Its totient is φ = 2688.

The previous prime is 4159. The next prime is 4177. The reversal of 4165 is 5614.

It can be written as a sum of positive squares in 2 ways, for example, as 2401 + 1764 = 49^2 + 42^2 .

It is not a de Polignac number, because 4165 - 2³ = 4157 is a prime.

It is an Ulam number.

It is an alternating number because its digits alternate between even and odd.

It is a Duffinian number.

4165 is a lucky number.

It is a plaindrome in base 15.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 4165.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 237 + ... + 253.

It is an arithmetic number, because the mean of its divisors is an integer number (513).

2⁴¹⁶⁵ is an apocalyptic number.

It is an amenable number.

4165 is a deficient number, since it is larger than the sum of its proper divisors (1991).

4165 is a wasteful number, since it uses less digits than its factorization.

4165 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 36 (or 29 counting only the distinct ones).

The product of its digits is 120, while the sum is 16.

The square root of 4165 is about 64.5368112011. The cubic root of 4165 is about 16.0893439253.

Adding to 4165 its reverse (5614), we get a palindrome (9779).

It can be divided in two parts, 416 and 5, that multiplied together give a triangular number (2080 = T₆₄).

The spelling of 4165 in words is "four thousand, one hundred sixty-five".