101606400000 has 1260 divisors, whose sum is σ = 441352810206. Its totient is φ = 23224320000.

The previous prime is 101606399981. The next prime is 101606400013. The reversal of 101606400000 is 4606101.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

101606400000 is a `hidden beast` number, since 10 + 16 + 0 + 640 + 0 + 0 + 0 + 0 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 146313216 + 101460086784 = 12096^2 + 318528^2 .

It is a tau number, because it is divible by the number of its divisors (1260).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 89 ways as a sum of consecutive naturals, for example, 14515199997 + ... + 14515200003.

Almost surely, 2^101606400000 is an apocalyptic number.

101606400000 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 101606400000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (220676405103).

101606400000 is an abundant number, since it is smaller than the sum of its proper divisors (339746410206).

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

101606400000 is an frugal number, since it uses more digits than its factorization.

101606400000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 77 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

The spelling of 101606400000 in words is "one hundred one billion, six hundred six million, four hundred thousand".