413221 has 4 divisors (see below), whose sum is σ = 427500. Its totient is φ = 398944.

The previous prime is 413207. The next prime is 413233. The reversal of 413221 is 122314.

It is a semiprime because it is the product of two primes.

It can be written as a sum of positive squares in 2 ways, for example, as 261121 + 152100 = 511^2 + 390^2 .

It is a cyclic number.

It is not a de Polignac number, because 413221 - 2⁷ = 413093 is a prime.

It is a Duffinian number.

413221 is a lucky number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413201) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 7096 + ... + 7153.

It is an arithmetic number, because the mean of its divisors is an integer number (106875).

2⁴¹³²²¹ is an apocalyptic number.

It is an amenable number.

413221 is a deficient number, since it is larger than the sum of its proper divisors (14279).

413221 is a wasteful number, since it uses less digits than its factorization.

413221 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 14278.

The product of its digits is 48, while the sum is 13.

The square root of 413221 is about 642.8226816160. The cubic root of 413221 is about 74.4836232640.

Adding to 413221 its reverse (122314), we get a palindrome (535535).

It can be divided in two parts, 4 and 13221, that added together give a square (13225 = 115²).

The spelling of 413221 in words is "four hundred thirteen thousand, two hundred twenty-one".