416385515520 has 720 divisors, whose sum is σ = 1613032905120. Its totient is φ = 102431195136.

The previous prime is 416385515479. The next prime is 416385515537. The reversal of 416385515520 is 25515583614.

416385515520 is a `hidden beast` number, since 4 + 1 + 6 + 3 + 85 + 515 + 52 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (720).

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

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 47 ways as a sum of consecutive naturals, for example, 258784476 + ... + 258786084.

Almost surely, 2^416385515520 is an apocalyptic number.

416385515520 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 416385515520, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (806516452560).

416385515520 is an abundant number, since it is smaller than the sum of its proper divisors (1196647389600).

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

416385515520 is an equidigital number, since it uses as much as digits as its factorization.

416385515520 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1670 (or 1632 counting only the distinct ones).

The product of its (nonzero) digits is 720000, while the sum is 45.

The spelling of 416385515520 in words is "four hundred sixteen billion, three hundred eighty-five million, five hundred fifteen thousand, five hundred twenty".