417813960096 has 288 divisors, whose sum is σ = 1357834907520. Its totient is φ = 120882972672.

The previous prime is 417813960077. The next prime is 417813960101. The reversal of 417813960096 is 690069318714.

417813960096 is a `hidden beast` number, since 4 + 17 + 8 + 13 + 9 + 600 + 9 + 6 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-2 number, since 2×417813960096² (a number of 24 digits) contains 22 as substring.

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 47 ways as a sum of consecutive naturals, for example, 5039490 + ... + 5121726.

It is an arithmetic number, because the mean of its divisors is an integer number (4714704540).

Almost surely, 2^417813960096 is an apocalyptic number.

417813960096 is a gapful number since it is divisible by the number (46) 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 417813960096, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (678917453760).

417813960096 is an abundant number, since it is smaller than the sum of its proper divisors (940020947424).

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

417813960096 is a wasteful number, since it uses less digits than its factorization.

417813960096 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 82348 (or 82337 counting only the distinct ones).

The product of its (nonzero) digits is 1959552, while the sum is 54.

The spelling of 417813960096 in words is "four hundred seventeen billion, eight hundred thirteen million, nine hundred sixty thousand, ninety-six".