413952 has 108 divisors (see below), whose sum is σ = 1398096. Its totient is φ = 107520.

The previous prime is 413951. The next prime is 413981. The reversal of 413952 is 259314.

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

It is an Ulam number.

It is a nialpdrome in base 16.

It is not an unprimeable number, because it can be changed into a prime (413951) 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 11 ways as a sum of consecutive naturals, for example, 37627 + ... + 37637.

2⁴¹³⁹⁵² is an apocalyptic number.

413952 is a gapful number since it is divisible by the number (42) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (699048).

413952 is an abundant number, since it is smaller than the sum of its proper divisors (984144).

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

413952 is a wasteful number, since it uses less digits than its factorization.

413952 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 44 (or 23 counting only the distinct ones).

The product of its digits is 1080, while the sum is 24.

The square root of 413952 is about 643.3910164123. The cubic root of 413952 is about 74.5275186240.

It can be divided in two parts, 41 and 3952, that added together give a palindrome (3993).

The spelling of 413952 in words is "four hundred thirteen thousand, nine hundred fifty-two".