416105012664 has 192 divisors, whose sum is σ = 1271445626880. Its totient is φ = 121795488000.

The previous prime is 416105012663. The next prime is 416105012671. The reversal of 416105012664 is 466210501614.

416105012664 is a `hidden beast` number, since 416 + 10 + 50 + 126 + 64 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (416105012663) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 13266969 + ... + 13298295.

It is an arithmetic number, because the mean of its divisors is an integer number (6622112640).

Almost surely, 2^416105012664 is an apocalyptic number.

416105012664 is a gapful number since it is divisible by the number (44) 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 416105012664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (635722813440).

416105012664 is an abundant number, since it is smaller than the sum of its proper divisors (855340614216).

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

416105012664 is a wasteful number, since it uses less digits than its factorization.

416105012664 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 31922 (or 31915 counting only the distinct ones).

The product of its (nonzero) digits is 34560, while the sum is 36.

It can be divided in two parts, 4161050 and 12664, that added together give a palindrome (4173714).

The spelling of 416105012664 in words is "four hundred sixteen billion, one hundred five million, twelve thousand, six hundred sixty-four".