137013408 has 288 divisors, whose sum is σ = 484848000. Its totient is φ = 36578304.

The previous prime is 137013403. The next prime is 137013439. The reversal of 137013408 is 804310731.

It is a tau number, because it is divible by the number of its divisors (288).

It is not an unprimeable number, because it can be changed into a prime (137013403) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1876860 + ... + 1876932.

It is an arithmetic number, because the mean of its divisors is an integer number (1683500).

Almost surely, 2^137013408 is an apocalyptic number.

137013408 is a gapful number since it is divisible by the number (18) 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 137013408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (242424000).

137013408 is an abundant number, since it is smaller than the sum of its proper divisors (347834592).

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

137013408 is a wasteful number, since it uses less digits than its factorization.

137013408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 129 (or 104 counting only the distinct ones).

The product of its (nonzero) digits is 2016, while the sum is 27.

The square root of 137013408 is about 11705.2726580802. The cubic root of 137013408 is about 515.5304905351.

The spelling of 137013408 in words is "one hundred thirty-seven million, thirteen thousand, four hundred eight".