103416405120 has 1152 divisors, whose sum is σ = 440794224000. Its totient is φ = 22231351296.

The previous prime is 103416405109. The next prime is 103416405151. The reversal of 103416405120 is 21504614301.

It is a happy number.

103416405120 is a `hidden beast` number, since 1 + 0 + 3 + 4 + 1 + 640 + 5 + 12 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 577745191 + ... + 577745369.

It is an arithmetic number, because the mean of its divisors is an integer number (382633875).

Almost surely, 2^103416405120 is an apocalyptic number.

103416405120 is a gapful number since it is divisible by the number (10) 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 103416405120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (220397112000).

103416405120 is an abundant number, since it is smaller than the sum of its proper divisors (337377818880).

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

103416405120 is a wasteful number, since it uses less digits than its factorization.

103416405120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 330 (or 308 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

It can be divided in two parts, 103416 and 405120, that added together give a triangular number (508536 = T₁₀₀₈).

The spelling of 103416405120 in words is "one hundred three billion, four hundred sixteen million, four hundred five thousand, one hundred twenty".