414193104 has 120 divisors (see below), whose sum is σ = 1261754312. Its totient is φ = 126074880.

The previous prime is 414193079. The next prime is 414193121. The reversal of 414193104 is 401391414.

It can be written as a sum of positive squares in 4 ways, for example, as 20250000 + 393943104 = 4500^2 + 19848^2 .

It is a congruent number.

It is an unprimeable number.

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, 180444 + ... + 182724.

Almost surely, 2^414193104 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 414193104, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (630877156).

414193104 is an abundant number, since it is smaller than the sum of its proper divisors (847561208).

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

414193104 is a wasteful number, since it uses less digits than its factorization.

414193104 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2405 (or 2396 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 414193104 is about 20351.7346680817. The cubic root of 414193104 is about 745.4198519286.

The spelling of 414193104 in words is "four hundred fourteen million, one hundred ninety-three thousand, one hundred four".