416138520 has 256 divisors, whose sum is σ = 1500871680. Its totient is φ = 90316800.

The previous prime is 416138509. The next prime is 416138521. The reversal of 416138520 is 25831614.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (416138521) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 1480780 + ... + 1481060.

It is an arithmetic number, because the mean of its divisors is an integer number (5862780).

Almost surely, 2^416138520 is an apocalyptic number.

416138520 is a gapful number since it is divisible by the number (40) 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 416138520, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (750435840).

416138520 is an abundant number, since it is smaller than the sum of its proper divisors (1084733160).

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

416138520 is a wasteful number, since it uses less digits than its factorization.

416138520 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 386 (or 382 counting only the distinct ones).

The product of its (nonzero) digits is 5760, while the sum is 30.

The square root of 416138520 is about 20399.4735226182. The cubic root of 416138520 is about 746.5850791310.

The spelling of 416138520 in words is "four hundred sixteen million, one hundred thirty-eight thousand, five hundred twenty".