412120400 has 60 divisors (see below), whose sum is σ = 1000020444. Its totient is φ = 163216000.

The previous prime is 412120391. The next prime is 412120411. The reversal of 412120400 is 4021214.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in 6 ways, for example, as 47004736 + 365115664 = 6856^2 + 19108^2 .

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 4080350 + ... + 4080450.

Almost surely, 2^412120400 is an apocalyptic number.

412120400 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 412120400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (500010222).

412120400 is an abundant number, since it is smaller than the sum of its proper divisors (587900044).

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

412120400 is an frugal number, since it uses more digits than its factorization.

412120400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 321 (or 108 counting only the distinct ones).

The product of its (nonzero) digits is 64, while the sum is 14.

The square root of 412120400 is about 20300.7487546642. The cubic root of 412120400 is about 744.1743627254.

Adding to 412120400 its reverse (4021214), we get a palindrome (416141614).

The spelling of 412120400 in words is "four hundred twelve million, one hundred twenty thousand, four hundred".