414164520 has 384 divisors, whose sum is σ = 1710858240. Its totient is φ = 84395520.

The previous prime is 414164459. The next prime is 414164561. The reversal of 414164520 is 25461414.

414164520 is a `hidden beast` number, since 4 + 14 + 1 + 645 + 2 + 0 = 666.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 1857129 + ... + 1857351.

It is an arithmetic number, because the mean of its divisors is an integer number (4455360).

Almost surely, 2^414164520 is an apocalyptic number.

414164520 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 414164520, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (855429120).

414164520 is an abundant number, since it is smaller than the sum of its proper divisors (1296693720).

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

414164520 is a wasteful number, since it uses less digits than its factorization.

414164520 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 325 (or 318 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

The square root of 414164520 is about 20351.0324062442. The cubic root of 414164520 is about 745.4027040725.

The spelling of 414164520 in words is "four hundred fourteen million, one hundred sixty-four thousand, five hundred twenty".