137416000 has 112 divisors (see below), whose sum is σ = 345917520. Its totient is φ = 54067200.

The previous prime is 137415989. The next prime is 137416021. The reversal of 137416000 is 614731.

It can be written as a sum of positive squares in 8 ways, for example, as 85229824 + 52186176 = 9232^2 + 7224^2 .

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 711904 + ... + 712096.

Almost surely, 2^137416000 is an apocalyptic number.

137416000 is a gapful number since it is divisible by the number (10) 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 137416000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (172958760).

137416000 is an abundant number, since it is smaller than the sum of its proper divisors (208501520).

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

137416000 is an equidigital number, since it uses as much as digits as its factorization.

137416000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 309 (or 289 counting only the distinct ones).

The product of its (nonzero) digits is 504, while the sum is 22.

The square root of 137416000 is about 11722.4570803224. The cubic root of 137416000 is about 516.0349314333.

The spelling of 137416000 in words is "one hundred thirty-seven million, four hundred sixteen thousand".