411312 has 80 divisors (see below), whose sum is σ = 1249920. Its totient is φ = 115200.

The previous prime is 411311. The next prime is 411337. The reversal of 411312 is 213114.

It is a happy number.

It is a super-3 number, since 3×411312³ = 208754283334569984, which contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (12).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

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 411312.

It is not an unprimeable number, because it can be changed into a prime (411311) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 10012 + ... + 10052.

It is an arithmetic number, because the mean of its divisors is an integer number (15624).

2⁴¹¹³¹² 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 411312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (624960).

411312 is an abundant number, since it is smaller than the sum of its proper divisors (838608).

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

411312 is a wasteful number, since it uses less digits than its factorization.

411312 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 82 (or 76 counting only the distinct ones).

The product of its digits is 24, while the sum is 12.

The square root of 411312 is about 641.3361053301. The cubic root of 411312 is about 74.3687462670.

Adding to 411312 its reverse (213114), we get a palindrome (624426).

The spelling of 411312 in words is "four hundred eleven thousand, three hundred twelve", and thus it is an iban number.