3006726105600 has 1440 divisors, whose sum is σ = 13006856079360. Its totient is φ = 647958528000.

The previous prime is 3006726105577. The next prime is 3006726105641. The reversal of 3006726105600 is 65016276003.

3006726105600 is a `hidden beast` number, since 3 + 0 + 0 + 67 + 26 + 10 + 560 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1440).

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

It is an unprimeable number.

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 143 ways as a sum of consecutive naturals, for example, 4765017285 + ... + 4765017915.

It is an arithmetic number, because the mean of its divisors is an integer number (9032538944).

Almost surely, 2^{3006726105600} is an apocalyptic number.

3006726105600 is a gapful number since it is divisible by the number (30) 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 3006726105600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (6503428039680).

3006726105600 is an abundant number, since it is smaller than the sum of its proper divisors (10000129973760).

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

3006726105600 is a wasteful number, since it uses less digits than its factorization.

3006726105600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1002 (or 978 counting only the distinct ones).

The product of its (nonzero) digits is 45360, while the sum is 36.

The spelling of 3006726105600 in words is "three trillion, six billion, seven hundred twenty-six million, one hundred five thousand, six hundred".