8001006128640 has 3200 divisors, whose sum is σ = 35877660825600. Its totient is φ = 1699574317056.

The previous prime is 8001006128587. The next prime is 8001006128651. The reversal of 8001006128640 is 468216001008.

8001006128640 is a `hidden beast` number, since 8 + 0 + 0 + 1 + 0 + 0 + 6 + 1 + 2 + 8 + 640 = 666.

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

It is a junction number, because it is equal to n+sod(n) for n = 8001006128595 and 8001006128604.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 319 ways as a sum of consecutive naturals, for example, 109602823644 + ... + 109602823716.

It is an arithmetic number, because the mean of its divisors is an integer number (11211769008).

Almost surely, 2^{8001006128640} is an apocalyptic number.

8001006128640 is a gapful number since it is divisible by the number (80) 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 8001006128640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17938830412800).

8001006128640 is an abundant number, since it is smaller than the sum of its proper divisors (27876654696960).

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

8001006128640 is an equidigital number, since it uses as much as digits as its factorization.

8001006128640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 219 (or 180 counting only the distinct ones).

The product of its (nonzero) digits is 18432, while the sum is 36.

The spelling of 8001006128640 in words is "eight trillion, one billion, six million, one hundred twenty-eight thousand, six hundred forty".