409917081600 has 864 divisors, whose sum is σ = 1620513858600. Its totient is φ = 98382643200.

The previous prime is 409917081589. The next prime is 409917081683. The reversal of 409917081600 is 6180719904.

It is a happy number.

It can be written as a sum of positive squares in 12 ways, for example, as 17780622336 + 392136459264 = 133344^2 + 626208^2 .

It is a super-2 number, since 2×409917081600² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 245605566 + ... + 245607234.

Almost surely, 2^409917081600 is an apocalyptic number.

409917081600 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 409917081600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (810256929300).

409917081600 is an abundant number, since it is smaller than the sum of its proper divisors (1210596777000).

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

409917081600 is a wasteful number, since it uses less digits than its factorization.

409917081600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1761 (or 1733 counting only the distinct ones).

The product of its (nonzero) digits is 108864, while the sum is 45.

The spelling of 409917081600 in words is "four hundred nine billion, nine hundred seventeen million, eighty-one thousand, six hundred".