416384188416 has 640 divisors, whose sum is σ = 1445876160960. Its totient is φ = 116955021312.

The previous prime is 416384188357. The next prime is 416384188457. The reversal of 416384188416 is 614881483614.

416384188416 is a `hidden beast` number, since 4 + 16 + 38 + 4 + 188 + 416 = 666.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a nude number because it is divisible by every one of its digits.

It is an unprimeable number.

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 39 ways as a sum of consecutive naturals, for example, 1356300135 + ... + 1356300441.

Almost surely, 2^416384188416 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 416384188416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (722938080480).

416384188416 is an abundant number, since it is smaller than the sum of its proper divisors (1029491972544).

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

416384188416 is an frugal number, since it uses more digits than its factorization.

416384188416 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 429 (or 392 counting only the distinct ones).

The product of its digits is 3538944, while the sum is 54.

The spelling of 416384188416 in words is "four hundred sixteen billion, three hundred eighty-four million, one hundred eighty-eight thousand, four hundred sixteen".