413316 has 48 divisors (see below), whose sum is σ = 1108800. Its totient is φ = 133056.

The previous prime is 413299. The next prime is 413353. The reversal of 413316 is 613314.

It is a Harshad number since it is a multiple of its sum of digits (18).

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

It is an unprimeable number.

413316 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 15 ways as a sum of consecutive naturals, for example, 4600 + ... + 4688.

It is an arithmetic number, because the mean of its divisors is an integer number (23100).

2⁴¹³³¹⁶ is an apocalyptic number.

413316 is the 344-th nonagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413316, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (554400).

413316 is an abundant number, since it is smaller than the sum of its proper divisors (695484).

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

413316 is a wasteful number, since it uses less digits than its factorization.

413316 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 145 (or 137 counting only the distinct ones).

The product of its digits is 216, while the sum is 18.

The square root of 413316 is about 642.8965702195. The cubic root of 413316 is about 74.4893307845.

It can be divided in two parts, 413 and 316, that added together give a 6-th power (729 = 3⁶).

The spelling of 413316 in words is "four hundred thirteen thousand, three hundred sixteen".