414146520 has 320 divisors, whose sum is σ = 1508569920. Its totient is φ = 101523456.

The previous prime is 414146489. The next prime is 414146527. The reversal of 414146520 is 25641414.

414146520 is a `hidden beast` number, since 4 + 1 + 4 + 1 + 4 + 652 + 0 = 666.

It is a super-2 number, since 2×414146520² = 343034680056220800, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414146527) by changing a digit.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 4020789 + ... + 4020891.

It is an arithmetic number, because the mean of its divisors is an integer number (4714281).

Almost surely, 2^414146520 is an apocalyptic number.

414146520 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 414146520, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (754284960).

414146520 is an abundant number, since it is smaller than the sum of its proper divisors (1094423400).

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

414146520 is a wasteful number, since it uses less digits than its factorization.

414146520 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 216 (or 203 counting only the distinct ones).

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

The square root of 414146520 is about 20350.5901634326. The cubic root of 414146520 is about 745.3919052696.

Adding to 414146520 its reverse (25641414), we get a palindrome (439787934).

The spelling of 414146520 in words is "four hundred fourteen million, one hundred forty-six thousand, five hundred twenty".