416805120 has 216 divisors, whose sum is σ = 1460875416. Its totient is φ = 109707264.

The previous prime is 416805119. The next prime is 416805121. The reversal of 416805120 is 21508614.

It is an interprime number because it is at equal distance from previous prime (416805119) and next prime (416805121).

It can be written as a sum of positive squares in 4 ways, for example, as 40755456 + 376049664 = 6384^2 + 19392^2 .

It is not an unprimeable number, because it can be changed into a prime (416805121) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1117254 + ... + 1117626.

Almost surely, 2^416805120 is an apocalyptic number.

416805120 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 416805120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (730437708).

416805120 is an abundant number, since it is smaller than the sum of its proper divisors (1044070296).

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

416805120 is a wasteful number, since it uses less digits than its factorization.

416805120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 497 (or 480 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 27.

The square root of 416805120 is about 20415.8056417081. The cubic root of 416805120 is about 746.9835106547.

The spelling of 416805120 in words is "four hundred sixteen million, eight hundred five thousand, one hundred twenty".