10005072000 has 512 divisors, whose sum is σ = 41366108160. Its totient is φ = 2078208000.

The previous prime is 10005071983. The next prime is 10005072001. The reversal of 10005072000 is 27050001.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is not an unprimeable number, because it can be changed into a prime (10005072001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 3694647 + ... + 3697353.

It is an arithmetic number, because the mean of its divisors is an integer number (80793180).

Almost surely, 2^10005072000 is an apocalyptic number.

10005072000 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

10005072000 is the 57750-th octagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10005072000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (20683054080).

10005072000 is an abundant number, since it is smaller than the sum of its proper divisors (31361036160).

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

10005072000 is a wasteful number, since it uses less digits than its factorization.

10005072000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2757 (or 2735 counting only the distinct ones).

The product of its (nonzero) digits is 70, while the sum is 15.

The spelling of 10005072000 in words is "ten billion, five million, seventy-two thousand".