413413000 has 384 divisors, whose sum is σ = 1344470400. Its totient is φ = 116928000.

The previous prime is 413412991. The next prime is 413413003. The reversal of 413413000 is 314314.

It is not an unprimeable number, because it can be changed into a prime (413413003) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 7006971 + ... + 7007029.

It is an arithmetic number, because the mean of its divisors is an integer number (3501225).

Almost surely, 2^413413000 is an apocalyptic number.

413413000 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 413413000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (672235200).

413413000 is an abundant number, since it is smaller than the sum of its proper divisors (931057400).

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

413413000 is a wasteful number, since it uses less digits than its factorization.

413413000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 118 (or 97 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 16.

The square root of 413413000 is about 20332.5600945872. The cubic root of 413413000 is about 744.9515756102.

Adding to 413413000 its reverse (314314), we get a palindrome (413727314).

The spelling of 413413000 in words is "four hundred thirteen million, four hundred thirteen thousand".