416164 has 24 divisors (see below), whose sum is σ = 846720. Its totient is φ = 175296.

The previous prime is 416159. The next prime is 416167. The reversal of 416164 is 461614.

416164 = 120² + 121² + ... + 143².

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (416167) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 2409 + ... + 2575.

It is an arithmetic number, because the mean of its divisors is an integer number (35280).

2⁴¹⁶¹⁶⁴ is an apocalyptic number.

It is an amenable number.

416164 is an abundant number, since it is smaller than the sum of its proper divisors (430556).

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

416164 is a wasteful number, since it uses less digits than its factorization.

416164 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 267 (or 265 counting only the distinct ones).

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

The square root of 416164 is about 645.1077429391. The cubic root of 416164 is about 74.6600316525.

Adding to 416164 its reverse (461614), we get a palindrome (877778).

It can be divided in two parts, 41616 and 4, that multiplied together give a square (166464 = 408²).

The spelling of 416164 in words is "four hundred sixteen thousand, one hundred sixty-four".