• 165 can be written using four 4's:

165 has 8 divisors (see below), whose sum is σ = 288. Its totient is φ = 80.

The previous prime is 163. The next prime is 167. The reversal of 165 is 561.

165 = T_{1} + T_{2} + ... +
T_{9}.

165 is nontrivially palindromic in base 2 and base 14.

165 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

165 is a nontrivial binomial coefficient, being equal to C(11, 3).

It is an interprime number because it is at equal distance from previous prime (163) and next prime (167).

It is a sphenic number, since it is the product of 3 distinct primes.

It is not a de Polignac number, because 165 - 2^{1} = 163 is a prime.

165 is an idoneal number.

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

It is a Curzon number.

165 is a nontrivial repdigit in base 14.

It is a plaindrome in base 8, base 12 and base 14.

It is a nialpdrome in base 4, base 6, base 13, base 14, base 15 and base 16.

It is a zygodrome in base 4 and base 14.

It is a self number, because there is not a number *n* which added to its sum of digits gives 165.

It is a congruent number.

It is the 9-th tetrahedral number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 10 + ... + 20.

It is an arithmetic number, because the mean of its divisors is an integer number (36).

165 is a gapful number since it is divisible by the number (15) formed by its first and last digit.

It is an amenable number.

165 is a deficient number, since it is larger than the sum of its proper divisors (123).

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

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

The sum of its prime factors is 19.

The product of its digits is 30, while the sum is 12.

The square root of 165 is about 12.8452325787. The cubic root of 165 is about 5.4848065524.

Subtracting from 165 its sum of digits (12), we obtain a triangular number (153 = T_{17}).

Multiplying 165 by its product of digits (30), we get a triangular number (4950 = T_{99}).

It can be divided in two parts, 16 and 5, that added together give a triangular number (21 = T_{6}).

The spelling of 165 in words is "one hundred sixty-five", and thus it is an aban number.

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