417949120512 has 1152 divisors, whose sum is σ = 1617846048000. Its totient is φ = 105345515520.

The previous prime is 417949120481. The next prime is 417949120517. The reversal of 417949120512 is 215021949714.

417949120512 is a `hidden beast` number, since 4 + 1 + 7 + 9 + 4 + 9 + 120 + 512 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (417949120517) by changing a digit.

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 95 ways as a sum of consecutive naturals, for example, 1102767939 + ... + 1102768317.

It is an arithmetic number, because the mean of its divisors is an integer number (1404380250).

Almost surely, 2^417949120512 is an apocalyptic number.

417949120512 is a gapful number since it is divisible by the number (42) 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 417949120512, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (808923024000).

417949120512 is an abundant number, since it is smaller than the sum of its proper divisors (1199896927488).

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

417949120512 is a wasteful number, since it uses less digits than its factorization.

417949120512 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 472 (or 439 counting only the distinct ones).

The product of its (nonzero) digits is 181440, while the sum is 45.

The spelling of 417949120512 in words is "four hundred seventeen billion, nine hundred forty-nine million, one hundred twenty thousand, five hundred twelve".