137528640 has 252 divisors, whose sum is σ = 510495804. Its totient is φ = 33865728.

The previous prime is 137528621. The next prime is 137528641. The reversal of 137528640 is 46825731.

137528640 is a `hidden beast` number, since 1 + 3 + 7 + 5 + 2 + 8 + 640 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 12446784 + 125081856 = 3528^2 + 11184^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a junction number, because it is equal to n+sod(n) for n = 137528595 and 137528604.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (137528641) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 2594854 + ... + 2594906.

It is an arithmetic number, because the mean of its divisors is an integer number (2025777).

Almost surely, 2^137528640 is an apocalyptic number.

137528640 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 137528640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (255247902).

137528640 is an abundant number, since it is smaller than the sum of its proper divisors (372967164).

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

137528640 is a wasteful number, since it uses less digits than its factorization.

137528640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 146 (or 80 counting only the distinct ones).

The product of its (nonzero) digits is 40320, while the sum is 36.

The square root of 137528640 is about 11727.2605496766. The cubic root of 137528640 is about 516.1758910010.

The spelling of 137528640 in words is "one hundred thirty-seven million, five hundred twenty-eight thousand, six hundred forty".