418129920 has 288 divisors, whose sum is σ = 1565109000. Its totient is φ = 102629376.

The previous prime is 418129871. The next prime is 418129927. The reversal of 418129920 is 29921814.

It can be written as a sum of positive squares in 4 ways, for example, as 308634624 + 109495296 = 17568^2 + 10464^2 .

It is a tau number, because it is divible by the number of its divisors (288).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (418129927) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1197906 + ... + 1198254.

Almost surely, 2^418129920 is an apocalyptic number.

418129920 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 418129920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (782554500).

418129920 is an abundant number, since it is smaller than the sum of its proper divisors (1146979080).

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

418129920 is a wasteful number, since it uses less digits than its factorization.

418129920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 395 (or 372 counting only the distinct ones).

The product of its (nonzero) digits is 10368, while the sum is 36.

The square root of 418129920 is about 20448.2253508709. The cubic root of 418129920 is about 747.7740936567.

The spelling of 418129920 in words is "four hundred eighteen million, one hundred twenty-nine thousand, nine hundred twenty".