138416040 has 320 divisors, whose sum is σ = 564537600. Its totient is φ = 29693952.

The previous prime is 138416039. The next prime is 138416051. The reversal of 138416040 is 40614831.

138416040 is a `hidden beast` number, since 13 + 8 + 41 + 604 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a junction number, because it is equal to n+sod(n) for n = 138415995 and 138416013.

It is an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 385381 + ... + 385739.

It is an arithmetic number, because the mean of its divisors is an integer number (1764180).

Almost surely, 2^138416040 is an apocalyptic number.

138416040 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 138416040, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (282268800).

138416040 is an abundant number, since it is smaller than the sum of its proper divisors (426121560).

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

138416040 is a wasteful number, since it uses less digits than its factorization.

138416040 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 406 (or 393 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 138416040 is about 11765.0346365831. The cubic root of 138416040 is about 517.2837155416.

It can be divided in two parts, 13841 and 6040, that added together give a square (19881 = 141²).

The spelling of 138416040 in words is "one hundred thirty-eight million, four hundred sixteen thousand, forty".