413540400 has 360 divisors, whose sum is σ = 1662591504. Its totient is φ = 87091200.

The previous prime is 413540399. The next prime is 413540443. The reversal of 413540400 is 4045314.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 764130 + ... + 764670.

Almost surely, 2^413540400 is an apocalyptic number.

413540400 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 413540400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (831295752).

413540400 is an abundant number, since it is smaller than the sum of its proper divisors (1249051104).

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

413540400 is a wasteful number, since it uses less digits than its factorization.

413540400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 589 (or 571 counting only the distinct ones).

The product of its (nonzero) digits is 960, while the sum is 21.

The square root of 413540400 is about 20335.6927592841. The cubic root of 413540400 is about 745.0280907685.

Adding to 413540400 its reverse (4045314), we get a palindrome (417585714).

The spelling of 413540400 in words is "four hundred thirteen million, five hundred forty thousand, four hundred".