137633580100 has 81 divisors (see below), whose sum is σ = 312408563383. Its totient is φ = 52627157440.

The previous prime is 137633580089. The next prime is 137633580121. The reversal of 137633580100 is 1085336731.

It is a happy number.

The square root of 137633580100 is 370990.

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 34128964 + 137599451136 = 5842^2 + 370944^2 .

It is a super-2 number, since 2×137633580100² (a number of 23 digits) contains 22 as substring.

It is a Duffinian number.

It is a self number, because there is not a number n which added to its sum of digits gives 137633580100.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 85326894 + ... + 85328506.

Almost surely, 2^137633580100 is an apocalyptic number.

137633580100 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

137633580100 is the 370990-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 137633580100

137633580100 is an abundant number, since it is smaller than the sum of its proper divisors (174774983283).

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

137633580100 is an equidigital number, since it uses as much as digits as its factorization.

137633580100 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3286 (or 1643 counting only the distinct ones).

The product of its (nonzero) digits is 45360, while the sum is 37.

The spelling of 137633580100 in words is "one hundred thirty-seven billion, six hundred thirty-three million, five hundred eighty thousand, one hundred".