413004032321 has 8 divisors (see below), whose sum is σ = 423091615464. Its totient is φ = 402917130880.

The previous prime is 413004032303. The next prime is 413004032323. The reversal of 413004032321 is 123230400314.

It can be written as a sum of positive squares in 4 ways, for example, as 130346993296 + 282657039025 = 361036^2 + 531655^2 .

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 413004032321 - 2⁶ = 413004032257 is a prime.

It is a super-2 number, since 2×413004032321² (a number of 24 digits) contains 22 as substring.

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (413004032323) 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, 1186355 + ... + 1494471.

It is an arithmetic number, because the mean of its divisors is an integer number (52886451933).

Almost surely, 2^413004032321 is an apocalyptic number.

413004032321 is a gapful number since it is divisible by the number (41) formed by its first and last digit.

It is an amenable number.

413004032321 is a deficient number, since it is larger than the sum of its proper divisors (10087583143).

413004032321 is a wasteful number, since it uses less digits than its factorization.

413004032321 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 340851.

The product of its (nonzero) digits is 1728, while the sum is 23.

Adding to 413004032321 its reverse (123230400314), we get a palindrome (536234432635).

The spelling of 413004032321 in words is "four hundred thirteen billion, four million, thirty-two thousand, three hundred twenty-one".