137408331736900 has 243 divisors, whose sum is σ = 349485308616087. Its totient is φ = 46757232144000.

The previous prime is 137408331736853. The next prime is 137408331736937. The reversal of 137408331736900 is 9637133804731.

The square root of 137408331736900 is 11722130.

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

It can be written as a sum of positive squares in 4 ways, for example, as 70684004834884 + 66724326902016 = 8407378^2 + 8168496^2 .

It is a super-2 number, since 2×137408331736900² (a number of 29 digits) contains 22 as substring.

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 123902913546 + ... + 123902914654.

Almost surely, 2^{137408331736900} is an apocalyptic number.

137408331736900 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

137408331736900 is the 11722130-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 137408331736900

137408331736900 is an abundant number, since it is smaller than the sum of its proper divisors (212076976879187).

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

137408331736900 is an equidigital number, since it uses as much as digits as its factorization.

137408331736900 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2548 (or 1274 counting only the distinct ones).

The product of its (nonzero) digits is 6858432, while the sum is 55.

The spelling of 137408331736900 in words is "one hundred thirty-seven trillion, four hundred eight billion, three hundred thirty-one million, seven hundred thirty-six thousand, nine hundred".