417420 has 48 divisors (see below), whose sum is σ = 1300320. Its totient is φ = 111168.

The previous prime is 417419. The next prime is 417437. The reversal of 417420 is 24714.

417420 = 82² + 83² + ... + 121².

It is a happy number.

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 = 417393 and 417402.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 417420.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 154 + ... + 926.

It is an arithmetic number, because the mean of its divisors is an integer number (27090).

2⁴¹⁷⁴²⁰ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 417420, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (650160).

417420 is an abundant number, since it is smaller than the sum of its proper divisors (882900).

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

417420 is a wasteful number, since it uses less digits than its factorization.

417420 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 791 (or 783 counting only the distinct ones).

The product of its (nonzero) digits is 224, while the sum is 18.

The square root of 417420 is about 646.0804903416. The cubic root of 417420 is about 74.7350652295.

It can be divided in two parts, 4 and 17420, that added together give a square (17424 = 132²).

The spelling of 417420 in words is "four hundred seventeen thousand, four hundred twenty", and thus it is an iban number.