413584 has 10 divisors (see below), whose sum is σ = 801350. Its totient is φ = 206784.

The previous prime is 413579. The next prime is 413587. The reversal of 413584 is 485314.

413584 = 12² + 13² + ... + 107².

It can be written as a sum of positive squares in only one way, i.e., 230400 + 183184 = 480^2 + 428^2 .

It is not an unprimeable number, because it can be changed into a prime (413587) by changing a digit.

413584 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 as a sum of consecutive naturals, namely, 12909 + ... + 12940.

It is an arithmetic number, because the mean of its divisors is an integer number (80135).

2⁴¹³⁵⁸⁴ is an apocalyptic number.

It is an amenable number.

413584 is a deficient number, since it is larger than the sum of its proper divisors (387766).

413584 is a wasteful number, since it uses less digits than its factorization.

413584 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 25857 (or 25851 counting only the distinct ones).

The product of its digits is 1920, while the sum is 25.

The square root of 413584 is about 643.1049681040. The cubic root of 413584 is about 74.5054272881.

Adding to 413584 its reverse (485314), we get a palindrome (898898).

The spelling of 413584 in words is "four hundred thirteen thousand, five hundred eighty-four".