137306000 has 80 divisors (see below), whose sum is σ = 357612528. Its totient is φ = 50688000.

The previous prime is 137305997. The next prime is 137306003. The reversal of 137306000 is 603731.

It is an interprime number because it is at equal distance from previous prime (137305997) and next prime (137306003).

It can be written as a sum of positive squares in 8 ways, for example, as 98168464 + 39137536 = 9908^2 + 6256^2 .

It is a tau number, because it is divible by the number of its divisors (80).

It is a Harshad number since it is a multiple of its sum of digits (20).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (137306003) by changing a digit.

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 15 ways as a sum of consecutive naturals, for example, 23360 + ... + 28640.

Almost surely, 2^137306000 is an apocalyptic number.

137306000 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 137306000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (178806264).

137306000 is an abundant number, since it is smaller than the sum of its proper divisors (220306528).

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

137306000 is a wasteful number, since it uses less digits than its factorization.

137306000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5317 (or 5301 counting only the distinct ones).

The product of its (nonzero) digits is 378, while the sum is 20.

The square root of 137306000 is about 11717.7642918775. The cubic root of 137306000 is about 515.8972012430.

Adding to 137306000 its reverse (603731), we get a palindrome (137909731).

The spelling of 137306000 in words is "one hundred thirty-seven million, three hundred six thousand".