413021000 has 96 divisors (see below), whose sum is σ = 1124393400. Its totient is φ = 141590400.

The previous prime is 413020957. The next prime is 413021009. The reversal of 413021000 is 120314.

It is a happy number.

It can be written as a sum of positive squares in 4 ways, for example, as 59505796 + 353515204 = 7714^2 + 18802^2 .

It is not an unprimeable number, because it can be changed into a prime (413021009) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 44786 + ... + 53214.

Almost surely, 2^413021000 is an apocalyptic number.

413021000 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413021000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (562196700).

413021000 is an abundant number, since it is smaller than the sum of its proper divisors (711372400).

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

413021000 is a wasteful number, since it uses less digits than its factorization.

413021000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 8464 (or 8443 counting only the distinct ones).

The product of its (nonzero) digits is 24, while the sum is 11.

The square root of 413021000 is about 20322.9180975568. The cubic root of 413021000 is about 744.7160457125.

Adding to 413021000 its reverse (120314), we get a palindrome (413141314).

The spelling of 413021000 in words is "four hundred thirteen million, twenty-one thousand".