34000409664 has 315 divisors, whose sum is σ = 109693964127. Its totient is φ = 10408559616.

The previous prime is 34000409633. The next prime is 34000409669. The reversal of 34000409664 is 46690400043.

The square root of 34000409664 is 184392.

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

It can be written as a sum of positive squares in 4 ways, for example, as 2116736064 + 31883673600 = 46008^2 + 178560^2 .

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

It is not an unprimeable number, because it can be changed into a prime (34000409669) by changing a digit.

It is a polite number, since it can be written in 44 ways as a sum of consecutive naturals, for example, 172590814 + ... + 172591010.

Almost surely, 2^34000409664 is an apocalyptic number.

34000409664 is the 184392-nd square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 34000409664

34000409664 is an abundant number, since it is smaller than the sum of its proper divisors (75693554463).

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

34000409664 is an equidigital number, since it uses as much as digits as its factorization.

34000409664 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 444 (or 215 counting only the distinct ones).

The product of its (nonzero) digits is 62208, while the sum is 36.

Multiplying 34000409664 by its sum of digits (36), we get a square (1224014747904 = 1106352²).

34000409664 divided by its sum of digits (36) gives a square (944455824 = 30732²).

The spelling of 34000409664 in words is "thirty-four billion, four hundred nine thousand, six hundred sixty-four".