34400414122100 has 144 divisors (see below), whose sum is σ = 81101074824000. Its totient is φ = 12589801835520.

The previous prime is 34400414122097. The next prime is 34400414122111. The reversal of 34400414122100 is 122141400443.

It is a super-2 number, since 2×34400414122100² (a number of 28 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (26).

It is a self number, because there is not a number n which added to its sum of digits gives 34400414122100.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 117221351 + ... + 117514449.

It is an arithmetic number, because the mean of its divisors is an integer number (563201908500).

Almost surely, 2^{34400414122100} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 34400414122100, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (40550537412000).

34400414122100 is an abundant number, since it is smaller than the sum of its proper divisors (46700660701900).

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

34400414122100 is a wasteful number, since it uses less digits than its factorization.

34400414122100 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 293922 (or 293915 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 26.

Adding to 34400414122100 its reverse (122141400443), we get a palindrome (34522555522543).

The spelling of 34400414122100 in words is "thirty-four trillion, four hundred billion, four hundred fourteen million, one hundred twenty-two thousand, one hundred".