349613201314080 has 2304 divisors, whose sum is σ = 1474649100288000. Its totient is φ = 74378723328000.

The previous prime is 349613201314079. The next prime is 349613201314087. The reversal of 349613201314080 is 80413102316943.

349613201314080 is a `hidden beast` number, since 3 + 4 + 9 + 6 + 1 + 3 + 201 + 31 + 408 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (349613201314087) by changing a digit.

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 383 ways as a sum of consecutive naturals, for example, 145007548075 + ... + 145007550485.

It is an arithmetic number, because the mean of its divisors is an integer number (640038672000).

Almost surely, 2^{349613201314080} is an apocalyptic number.

349613201314080 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 349613201314080, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (737324550144000).

349613201314080 is an abundant number, since it is smaller than the sum of its proper divisors (1125035898973920).

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

349613201314080 is a wasteful number, since it uses less digits than its factorization.

349613201314080 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3119 (or 3108 counting only the distinct ones).

The product of its (nonzero) digits is 373248, while the sum is 45.

The spelling of 349613201314080 in words is "three hundred forty-nine trillion, six hundred thirteen billion, two hundred one million, three hundred fourteen thousand, eighty".