414414 has 96 divisors (see below), whose sum is σ = 1257984. Its totient is φ = 95040.

The previous prime is 414413. The next prime is 414431.

Added to its reverse (414414) it gives a triangular number (828828 = T₁₂₈₇).

414414 is nontrivially palindromic in base 10.

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

It is a Curzon number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414413) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 18007 + ... + 18029.

It is an arithmetic number, because the mean of its divisors is an integer number (13104).

2⁴¹⁴⁴¹⁴ is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 414414, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (628992).

414414 is an abundant number, since it is smaller than the sum of its proper divisors (843570).

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

414414 is a wasteful number, since it uses less digits than its factorization.

414414 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 62 (or 59 counting only the distinct ones).

The product of its digits is 256, while the sum is 18.

The square root of 414414 is about 643.7499514563. The cubic root of 414414 is about 74.5552343270. Note that the first 3 decimals are identical.

It can be divided in two parts, 414 and 414, that added together give a palindrome (828).

The spelling of 414414 in words is "four hundred fourteen thousand, four hundred fourteen", and thus it is an iban number.