408121612080400 has 405 divisors, whose sum is σ = 1011450606698343. Its totient is φ = 158254543872000.

The previous prime is 408121612080389. The next prime is 408121612080419. The reversal of 408121612080400 is 4080216121804.

The square root of 408121612080400 is 20202020.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 40 ways, for example, as 278050689221904 + 130070922858496 = 16674852^2 + 11404864^2 .

It is a self number, because there is not a number n which added to its sum of digits gives 408121612080400.

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 2978989869132 + ... + 2978989869268.

Almost surely, 2^{408121612080400} is an apocalyptic number.

408121612080400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

408121612080400 is the 20202020-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 408121612080400

408121612080400 is an abundant number, since it is smaller than the sum of its proper divisors (603328994617943).

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

408121612080400 is an equidigital number, since it uses as much as digits as its factorization.

408121612080400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 640 (or 318 counting only the distinct ones).

The product of its (nonzero) digits is 24576, while the sum is 37.

The spelling of 408121612080400 in words is "four hundred eight trillion, one hundred twenty-one billion, six hundred twelve million, eighty thousand, four hundred".