137728512 has 180 divisors, whose sum is σ = 422828406. Its totient is φ = 44789760.

The previous prime is 137728499. The next prime is 137728519. The reversal of 137728512 is 215827731.

137728512 is a `hidden beast` number, since 1 + 377 + 285 + 1 + 2 = 666.

It can be written as a sum of positive squares in only one way, i.e., 136048896 + 1679616 = 11664^2 + 1296^2 .

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

It is not an unprimeable number, because it can be changed into a prime (137728519) by changing a digit.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 3359212 + ... + 3359252.

Almost surely, 2^137728512 is an apocalyptic number.

137728512 is a gapful number since it is divisible by the number (12) 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 137728512, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (211414203).

137728512 is an abundant number, since it is smaller than the sum of its proper divisors (285099894).

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

137728512 is an frugal number, since it uses more digits than its factorization.

137728512 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 83 (or 46 counting only the distinct ones).

The product of its digits is 23520, while the sum is 36.

The square root of 137728512 is about 11735.7791390261. The cubic root of 137728512 is about 516.4258248064.

The spelling of 137728512 in words is "one hundred thirty-seven million, seven hundred twenty-eight thousand, five hundred twelve".