1009006416000 has 1536 divisors, whose sum is σ = 4147940160000. Its totient is φ = 240869376000.

The previous prime is 1009006415987. The next prime is 1009006416037. The reversal of 1009006416000 is 6146009001.

1009006416000 is a `hidden beast` number, since 10 + 0 + 9 + 0 + 0 + 6 + 41 + 600 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (27).

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 191 ways as a sum of consecutive naturals, for example, 5070383901 + ... + 5070384099.

It is an arithmetic number, because the mean of its divisors is an integer number (2700481875).

Almost surely, 2^{1009006416000} is an apocalyptic number.

1009006416000 is a gapful number since it is divisible by the number (10) 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 1009006416000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2073970080000).

1009006416000 is an abundant number, since it is smaller than the sum of its proper divisors (3138933744000).

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

1009006416000 is a wasteful number, since it uses less digits than its factorization.

1009006416000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 356 (or 317 counting only the distinct ones).

The product of its (nonzero) digits is 1296, while the sum is 27.

The spelling of 1009006416000 in words is "one trillion, nine billion, six million, four hundred sixteen thousand".