406405120 has 180 divisors, whose sum is σ = 1098218772. Its totient is φ = 144179200.

The previous prime is 406405091. The next prime is 406405123. The reversal of 406405120 is 21504604.

It can be written as a sum of positive squares in 2 ways, for example, as 71368704 + 335036416 = 8448^2 + 18304^2 .

It is a Harshad number since it is a multiple of its sum of digits (22).

It is a junction number, because it is equal to n+sod(n) for n = 406405091 and 406405100.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (406405123) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 9912300 + ... + 9912340.

Almost surely, 2^406405120 is an apocalyptic number.

406405120 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 406405120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (549109386).

406405120 is an abundant number, since it is smaller than the sum of its proper divisors (691813652).

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

406405120 is an equidigital number, since it uses as much as digits as its factorization.

406405120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 96 (or 59 counting only the distinct ones).

The product of its (nonzero) digits is 960, while the sum is 22.

The square root of 406405120 is about 20159.4920570931. The cubic root of 406405120 is about 740.7182702122.

Adding to 406405120 its reverse (21504604), we get a palindrome (427909724).

The spelling of 406405120 in words is "four hundred six million, four hundred five thousand, one hundred twenty".