413688 has 32 divisors (see below), whose sum is σ = 1128960. Its totient is φ = 125280.

The previous prime is 413683. The next prime is 413689. The reversal of 413688 is 886314.

It is a happy number.

It is a super-2 number, since 2×413688² = 342275522688, which contains 22 as substring.

It is a Smith number, since the sum of its digits (30) coincides with the sum of the digits of its prime factors.

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 inconsummate number, since it does not exist a number n which divided by its sum of digits gives 413688.

It is not an unprimeable number, because it can be changed into a prime (413681) by changing a digit.

413688 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 520 + ... + 1047.

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

2⁴¹³⁶⁸⁸ is an apocalyptic number.

It is an amenable number.

413688 is an abundant number, since it is smaller than the sum of its proper divisors (715272).

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

413688 is a wasteful number, since it uses less digits than its factorization.

413688 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1587 (or 1583 counting only the distinct ones).

The product of its digits is 4608, while the sum is 30.

The square root of 413688 is about 643.1858207392. The cubic root of 413688 is about 74.5116718196.

It can be divided in two parts, 4136 and 88, that added together give a palindrome (4224).

The spelling of 413688 in words is "four hundred thirteen thousand, six hundred eighty-eight".