409612800100 has 243 divisors, whose sum is σ = 1064587696011. Its totient is φ = 136398931200.

The previous prime is 409612800067. The next prime is 409612800127. The reversal of 409612800100 is 1008216904.

It is a happy number.

The square root of 409612800100 is 640010.

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

It can be written as a sum of positive squares in 4 ways, for example, as 172412631076 + 237200169024 = 415226^2 + 487032^2 .

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, 1836828589 + ... + 1836828811.

Almost surely, 2^409612800100 is an apocalyptic number.

409612800100 is the 640010-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 409612800100

409612800100 is an abundant number, since it is smaller than the sum of its proper divisors (654974895911).

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

409612800100 is a wasteful number, since it uses less digits than its factorization.

409612800100 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 556 (or 278 counting only the distinct ones).

The product of its (nonzero) digits is 3456, while the sum is 31.

The spelling of 409612800100 in words is "four hundred nine billion, six hundred twelve million, eight hundred thousand, one hundred".