413749600 has 72 divisors (see below), whose sum is σ = 1101913848. Its totient is φ = 150451200.

The previous prime is 413749571. The next prime is 413749603. The reversal of 413749600 is 6947314.

It is a happy number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413749603) 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 11 ways as a sum of consecutive naturals, for example, 14709 + ... + 32308.

It is an arithmetic number, because the mean of its divisors is an integer number (15304359).

Almost surely, 2^413749600 is an apocalyptic number.

413749600 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

413749600 is an abundant number, since it is smaller than the sum of its proper divisors (688164248).

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

413749600 is a wasteful number, since it uses less digits than its factorization.

413749600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 47048 (or 47035 counting only the distinct ones).

The product of its (nonzero) digits is 18144, while the sum is 34.

The square root of 413749600 is about 20340.8357743727. The cubic root of 413749600 is about 745.1537001020.

The spelling of 413749600 in words is "four hundred thirteen million, seven hundred forty-nine thousand, six hundred".