413321 has 8 divisors (see below), whose sum is σ = 449064. Its totient is φ = 378880.

The previous prime is 413299. The next prime is 413353. The reversal of 413321 is 123314.

413321 = T₁₂₁ + T₁₂₂ + ... + T₁₆₁.

It can be written as a sum of positive squares in 4 ways, for example, as 40000 + 373321 = 200^2 + 611^2 .

It is a sphenic number, since it is the product of 3 distinct primes.

It is a cyclic number.

It is not a de Polignac number, because 413321 - 2¹⁴ = 396937 is a prime.

It is a Duffinian number.

It is a junction number, because it is equal to n+sod(n) for n = 413296 and 413305.

It is not an unprimeable number, because it can be changed into a prime (413521) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 401 + ... + 993.

It is an arithmetic number, because the mean of its divisors is an integer number (56133).

2⁴¹³³²¹ is an apocalyptic number.

413321 is a gapful number since it is divisible by the number (41) formed by its first and last digit.

It is an amenable number.

413321 is a deficient number, since it is larger than the sum of its proper divisors (35743).

413321 is a wasteful number, since it uses less digits than its factorization.

413321 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 651.

The product of its digits is 72, while the sum is 14.

The square root of 413321 is about 642.9004588581. The cubic root of 413321 is about 74.4896311561.

Adding to 413321 its reverse (123314), we get a palindrome (536635).

It can be divided in two parts, 41 and 3321, that multiplied together give a square (136161 = 369²).

The spelling of 413321 in words is "four hundred thirteen thousand, three hundred twenty-one".