414120 has 128 divisors (see below), whose sum is σ = 1555200. Its totient is φ = 86016.

The previous prime is 414109. The next prime is 414131. The reversal of 414120 is 21414.

414120 = T₁₃₆ + T₁₃₇ + ... + T₁₇₀.

414120 = 148² + 149² + ... + 164².

It is an interprime number because it is at equal distance from previous prime (414109) and next prime (414131).

It is a super-3 number, since 3×414120³ = 213058993339584000, which contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (12).

It is a zygodrome in base 13.

It is a junction number, because it is equal to n+sod(n) for n = 414096 and 414105.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 414120.

It is an unprimeable number.

414120 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 14266 + ... + 14294.

It is an arithmetic number, because the mean of its divisors is an integer number (12150).

2⁴¹⁴¹²⁰ is an apocalyptic number.

414120 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 414120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (777600).

414120 is an abundant number, since it is smaller than the sum of its proper divisors (1141080).

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

414120 is a wasteful number, since it uses less digits than its factorization.

414120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 67 (or 63 counting only the distinct ones).

The product of its (nonzero) digits is 32, while the sum is 12.

The square root of 414120 is about 643.5215614103. The cubic root of 414120 is about 74.5375994463.

Adding to 414120 its reverse (21414), we get a palindrome (435534).

The spelling of 414120 in words is "four hundred fourteen thousand, one hundred twenty", and thus it is an iban number.