83413468293120 has 1536 divisors, whose sum is σ = 348270354432000. Its totient is φ = 18540810731520.

The previous prime is 83413468293083. The next prime is 83413468293121. The reversal of 83413468293120 is 2139286431438.

83413468293120 is a `hidden beast` number, since 8 + 3 + 4 + 1 + 346 + 8 + 293 + 1 + 2 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1536).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is not an unprimeable number, because it can be changed into a prime (83413468293121) by changing a digit.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 20056133601 + ... + 20056137759.

It is an arithmetic number, because the mean of its divisors is an integer number (226738512000).

Almost surely, 2^{83413468293120} is an apocalyptic number.

83413468293120 is a gapful number since it is divisible by the number (80) 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 83413468293120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (174135177216000).

83413468293120 is an abundant number, since it is smaller than the sum of its proper divisors (264856886138880).

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

83413468293120 is a wasteful number, since it uses less digits than its factorization.

83413468293120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 4486 (or 4460 counting only the distinct ones).

The product of its (nonzero) digits is 5971968, while the sum is 54.

The spelling of 83413468293120 in words is "eighty-three trillion, four hundred thirteen billion, four hundred sixty-eight million, two hundred ninety-three thousand, one hundred twenty".