34000041600 has 720 divisors, whose sum is σ = 146006662230. Its totient is φ = 7768535040.

The previous prime is 34000041577. The next prime is 34000041631. The reversal of 34000041600 is 614000043.

It can be written as a sum of positive squares in 3 ways, for example, as 14509647936 + 19490393664 = 120456^2 + 139608^2 .

It is a tau number, because it is divible by the number of its divisors (720).

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 (19) of ones.

It is a polite number, since it can be written in 89 ways as a sum of consecutive naturals, for example, 12699462 + ... + 12702138.

Almost surely, 2^34000041600 is an apocalyptic number.

34000041600 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 34000041600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (73003331115).

34000041600 is an abundant number, since it is smaller than the sum of its proper divisors (112006620630).

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

34000041600 is a wasteful number, since it uses less digits than its factorization.

34000041600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2727 (or 2694 counting only the distinct ones).

The product of its (nonzero) digits is 288, while the sum is 18.

Adding to 34000041600 its reverse (614000043), we get a palindrome (34614041643).

The spelling of 34000041600 in words is "thirty-four billion, forty-one thousand, six hundred".