416199168 has 640 divisors, whose sum is σ = 1697034240. Its totient is φ = 97320960.

The previous prime is 416199143. The next prime is 416199197. The reversal of 416199168 is 861991614.

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

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 63 ways as a sum of consecutive naturals, for example, 18095605 + ... + 18095627.

It is an arithmetic number, because the mean of its divisors is an integer number (2651616).

Almost surely, 2^416199168 is an apocalyptic number.

416199168 is a gapful number since it is divisible by the number (48) formed by its first and last digit.

416199168 is the 12903-rd heptagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 416199168, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (848517120).

416199168 is an abundant number, since it is smaller than the sum of its proper divisors (1280835072).

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

416199168 is a wasteful number, since it uses less digits than its factorization.

416199168 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 85 (or 63 counting only the distinct ones).

The product of its digits is 93312, while the sum is 45.

The square root of 416199168 is about 20400.9599774128. The cubic root of 416199168 is about 746.6213464556.

The spelling of 416199168 in words is "four hundred sixteen million, one hundred ninety-nine thousand, one hundred sixty-eight".