413964 has 24 divisors (see below), whose sum is σ = 1073520. Its totient is φ = 137952.

The previous prime is 413951. The next prime is 413981. The reversal of 413964 is 469314.

It is a Harshad number since it is a multiple of its sum of digits (27).

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

It is an unprimeable number.

413964 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1809 + ... + 2024.

It is an arithmetic number, because the mean of its divisors is an integer number (44730).

2⁴¹³⁹⁶⁴ is an apocalyptic number.

It is an amenable number.

413964 is an abundant number, since it is smaller than the sum of its proper divisors (659556).

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

413964 is a wasteful number, since it uses less digits than its factorization.

413964 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3846 (or 3838 counting only the distinct ones).

The product of its digits is 2592, while the sum is 27.

The square root of 413964 is about 643.4003419334. The cubic root of 413964 is about 74.5282387732.

It can be divided in two parts, 41 and 3964, that added together give a triangular number (4005 = T₈₉).

The spelling of 413964 in words is "four hundred thirteen thousand, nine hundred sixty-four".