413712 has 90 divisors (see below), whose sum is σ = 1327482. Its totient is φ = 119808.

The previous prime is 413711. The next prime is 413713. The reversal of 413712 is 217314.

It is an interprime number because it is at equal distance from previous prime (413711) and next prime (413713).

It can be written as a sum of positive squares in 3 ways, for example, as 9216 + 404496 = 96^2 + 636^2 .

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

It is a plaindrome in base 14.

It is not an unprimeable number, because it can be changed into a prime (413711) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 24328 + ... + 24344.

2⁴¹³⁷¹² 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 413712, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (663741).

413712 is an abundant number, since it is smaller than the sum of its proper divisors (913770).

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

413712 is a wasteful number, since it uses less digits than its factorization.

413712 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 57 (or 35 counting only the distinct ones).

The product of its digits is 168, while the sum is 18.

The square root of 413712 is about 643.2044775964. The cubic root of 413712 is about 74.5131127167.

The spelling of 413712 in words is "four hundred thirteen thousand, seven hundred twelve".