137728416 has 288 divisors, whose sum is σ = 468840960. Its totient is φ = 35126784.

The previous prime is 137728411. The next prime is 137728421. The reversal of 137728416 is 614827731.

It is an interprime number because it is at equal distance from previous prime (137728411) and next prime (137728421).

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (137728411) 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, 2055615 + ... + 2055681.

It is an arithmetic number, because the mean of its divisors is an integer number (1627920).

Almost surely, 2^137728416 is an apocalyptic number.

137728416 is a gapful number since it is divisible by the number (16) 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 137728416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (234420480).

137728416 is an abundant number, since it is smaller than the sum of its proper divisors (331112544).

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

137728416 is a wasteful number, since it uses less digits than its factorization.

137728416 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 136 (or 121 counting only the distinct ones).

The product of its digits is 56448, while the sum is 39.

The square root of 137728416 is about 11735.7750489689. The cubic root of 137728416 is about 516.4257048194.

The spelling of 137728416 in words is "one hundred thirty-seven million, seven hundred twenty-eight thousand, four hundred sixteen".