414213120 has 264 divisors, whose sum is σ = 1465733880. Its totient is φ = 108134400.

The previous prime is 414213101. The next prime is 414213197. The reversal of 414213120 is 21312414.

It can be written as a sum of positive squares in 4 ways, for example, as 78004224 + 336208896 = 8832^2 + 18336^2 .

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a junction number, because it is equal to n+sod(n) for n = 414213093 and 414213102.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 4101070 + ... + 4101170.

Almost surely, 2^414213120 is an apocalyptic number.

414213120 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 414213120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (732866940).

414213120 is an abundant number, since it is smaller than the sum of its proper divisors (1051520760).

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

414213120 is a wasteful number, since it uses less digits than its factorization.

414213120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 221 (or 200 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 414213120 is about 20352.2264138349. The cubic root of 414213120 is about 745.4318592775.

Adding to 414213120 its reverse (21312414), we get a palindrome (435525534).

The spelling of 414213120 in words is "four hundred fourteen million, two hundred thirteen thousand, one hundred twenty".