414090 has 48 divisors (see below), whose sum is σ = 1111968. Its totient is φ = 106848.

The previous prime is 414083. The next prime is 414097. The reversal of 414090 is 90414.

414090 = 1² + 2² + ... + 107².

It is an interprime number because it is at equal distance from previous prime (414083) and next prime (414097).

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

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 414090.

It is not an unprimeable number, because it can be changed into a prime (414097) by changing a digit.

414090 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 23 ways as a sum of consecutive naturals, for example, 3817 + ... + 3923.

It is an arithmetic number, because the mean of its divisors is an integer number (23166).

2⁴¹⁴⁰⁹⁰ is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 414090, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (555984).

414090 is an abundant number, since it is smaller than the sum of its proper divisors (697878).

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

414090 is a wasteful number, since it uses less digits than its factorization.

414090 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 163 (or 160 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

The square root of 414090 is about 643.4982517459. The cubic root of 414090 is about 74.5357994995.

414090 divided by its sum of digits (18) gives a triangular number (23005 = T₂₁₄).

The spelling of 414090 in words is "four hundred fourteen thousand, ninety".