413664 has 48 divisors (see below), whose sum is σ = 1128960. Its totient is φ = 132480.

The previous prime is 413653. The next prime is 413681. The reversal of 413664 is 466314.

It is a tau number, because it is divible by the number of its divisors (48).

It is a super-2 number, since 2×413664² = 342235809792, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a nude number because it is divisible by every one of its digits.

It is a nialpdrome in base 14.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 2907 + ... + 3045.

It is an arithmetic number, because the mean of its divisors is an integer number (23520).

2⁴¹³⁶⁶⁴ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (564480).

413664 is an abundant number, since it is smaller than the sum of its proper divisors (715296).

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

413664 is a wasteful number, since it uses less digits than its factorization.

413664 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 183 (or 175 counting only the distinct ones).

The product of its digits is 1728, while the sum is 24.

The square root of 413664 is about 643.1671633409. The cubic root of 413664 is about 74.5102308668.

Adding to 413664 its reverse (466314), we get a palindrome (879978).

Subtracting 413664 from its reverse (466314), we obtain a triangular number (52650 = T₃₂₄).

The spelling of 413664 in words is "four hundred thirteen thousand, six hundred sixty-four".