413038416 has 320 divisors, whose sum is σ = 1399910400. Its totient is φ = 102187008.

The previous prime is 413038411. The next prime is 413038429. The reversal of 413038416 is 614830314.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413038411) by changing a digit.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 4258080 + ... + 4258176.

It is an arithmetic number, because the mean of its divisors is an integer number (4374720).

Almost surely, 2^413038416 is an apocalyptic number.

413038416 is a gapful number since it is divisible by the number (46) 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 413038416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (699955200).

413038416 is an abundant number, since it is smaller than the sum of its proper divisors (986871984).

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

413038416 is a wasteful number, since it uses less digits than its factorization.

413038416 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 186 (or 180 counting only the distinct ones).

The product of its (nonzero) digits is 6912, while the sum is 30.

The square root of 413038416 is about 20323.3465748139. The cubic root of 413038416 is about 744.7265131321.

The spelling of 413038416 in words is "four hundred thirteen million, thirty-eight thousand, four hundred sixteen".