413601408 has 192 divisors, whose sum is σ = 1313694720. Its totient is φ = 123863040.

The previous prime is 413601407. The next prime is 413601413. The reversal of 413601408 is 804106314.

413601408 is a `hidden beast` number, since 4 + 13 + 601 + 40 + 8 = 666.

It is a tau number, because it is divible by the number of its divisors (192).

It is a super-2 number, since 2×413601408² = 342132249399164928, which contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413601403) 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 23 ways as a sum of consecutive naturals, for example, 1609216 + ... + 1609472.

It is an arithmetic number, because the mean of its divisors is an integer number (6842160).

Almost surely, 2^413601408 is an apocalyptic number.

413601408 is a gapful number since it is divisible by the number (48) 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 413601408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (656847360).

413601408 is an abundant number, since it is smaller than the sum of its proper divisors (900093312).

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

413601408 is a wasteful number, since it uses less digits than its factorization.

413601408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 415 (or 400 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 413601408 is about 20337.1927266277. The cubic root of 413601408 is about 745.0647259951.

The spelling of 413601408 in words is "four hundred thirteen million, six hundred one thousand, four hundred eight".