329039904400 has 405 divisors, whose sum is σ = 876228324699. Its totient is φ = 118725573120.

The previous prime is 329039904283. The next prime is 329039904439. The reversal of 329039904400 is 4409930923.

The square root of 329039904400 is 573620.

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 4522831504 + 324517072896 = 67252^2 + 569664^2 .

It is a super-2 number, since 2×329039904400² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (43).

It is a Duffinian number.

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 80 ways as a sum of consecutive naturals, for example, 7652090779 + ... + 7652090821.

Almost surely, 2^329039904400 is an apocalyptic number.

329039904400 is the 573620-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 329039904400

329039904400 is an abundant number, since it is smaller than the sum of its proper divisors (547188420299).

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

329039904400 is a wasteful number, since it uses less digits than its factorization.

329039904400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 208 (or 102 counting only the distinct ones).

The product of its (nonzero) digits is 209952, while the sum is 43.

The spelling of 329039904400 in words is "three hundred twenty-nine billion, thirty-nine million, nine hundred four thousand, four hundred".