729723347345664 has 567 divisors, whose sum is σ = 2540734035025053. Its totient is φ = 208469045385216.

The previous prime is 729723347345653. The next prime is 729723347345701. The reversal of 729723347345664 is 466543743327927.

The square root of 729723347345664 is 27013392.

It is a perfect power (a square), and thus also a powerful number.

729723347345664 is a `hidden beast` number, since 7 + 2 + 9 + 7 + 23 + 3 + 4 + 7 + 34 + 566 + 4 = 666.

It can be written as a sum of positive squares in only one way, i.e., 186414239289600 + 543309108056064 = 13653360^2 + 23308992^2 .

It is a tau number, because it is divible by the number of its divisors (567).

It is a super-2 number, since 2×729723347345664² (a number of 31 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is a junction number, because it is equal to n+sod(n) for n = 729723347345592 and 729723347345601.

It is an unprimeable number.

It is a polite number, since it can be written in 62 ways as a sum of consecutive naturals, for example, 81688492942 + ... + 81688501874.

Almost surely, 2^{729723347345664} is an apocalyptic number.

729723347345664 is the 27013392-nd square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 729723347345664

729723347345664 is an abundant number, since it is smaller than the sum of its proper divisors (1811010687679389).

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

729723347345664 is an frugal number, since it uses more digits than its factorization.

729723347345664 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 17914 (or 8945 counting only the distinct ones).

The product of its digits is 3840721920, while the sum is 72.

The spelling of 729723347345664 in words is "seven hundred twenty-nine trillion, seven hundred twenty-three billion, three hundred forty-seven million, three hundred forty-five thousand, six hundred sixty-four".