164164 has 48 divisors (see below), whose sum is σ = 395136. Its totient is φ = 57600.

The previous prime is 164149. The next prime is 164173. The reversal of 164164 is 461461.

164164 = T₁₁₁ + T₁₁₂ + ... + T₁₃₂.

It is a Smith number, since the sum of its digits (22) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (22).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 3984 + ... + 4024.

It is an arithmetic number, because the mean of its divisors is an integer number (8232).

2¹⁶⁴¹⁶⁴ is an apocalyptic number.

164164 is a gapful number since it is divisible by the number (14) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 164164, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (197568).

164164 is an abundant number, since it is smaller than the sum of its proper divisors (230972).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

164164 is a wasteful number, since it uses less digits than its factorization.

164164 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 76 (or 74 counting only the distinct ones).

The product of its digits is 576, while the sum is 22.

The square root of 164164 is about 405.1715685978. The cubic root of 164164 is about 54.7552763484.

The spelling of 164164 in words is "one hundred sixty-four thousand, one hundred sixty-four".