349549390137600 has 1215 divisors, whose sum is σ = 1352277498045243. Its totient is φ = 89081451233280.

The previous prime is 349549390137559. The next prime is 349549390137601. The reversal of 349549390137600 is 6731093945943.

The square root of 349549390137600 is 18696240.

It is a perfect power (a square), and thus also a powerful number.

349549390137600 is a `hidden beast` number, since 3 + 4 + 9 + 5 + 4 + 9 + 3 + 9 + 0 + 13 + 7 + 600 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 121857224898816 + 227692165238784 = 11038896^2 + 15089472^2 .

It is a super-2 number, since 2×349549390137600² (a number of 30 digits) contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (349549390137601) by changing a digit.

It is a polite number, since it can be written in 134 ways as a sum of consecutive naturals, for example, 309609733836 + ... + 309609734964.

Almost surely, 2^{349549390137600} is an apocalyptic number.

349549390137600 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

349549390137600 is the 18696240-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 349549390137600

349549390137600 is an abundant number, since it is smaller than the sum of its proper divisors (1002728107907643).

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

349549390137600 is an frugal number, since it uses more digits than its factorization.

349549390137600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2342 (or 1162 counting only the distinct ones).

The product of its (nonzero) digits is 66134880, while the sum is 63.

The spelling of 349549390137600 in words is "three hundred forty-nine trillion, five hundred forty-nine billion, three hundred ninety million, one hundred thirty-seven thousand, six hundred".