413513100 has 864 divisors, whose sum is σ = 1910877696. Its totient is φ = 74649600.

The previous prime is 413513071. The next prime is 413513101. The reversal of 413513100 is 1315314.

413513100 is a `hidden beast` number, since 4 + 1 + 351 + 310 + 0 = 666.

It is a super-2 number, since 2×413513100² = 341986167743220000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413513101) by changing a digit.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 24324292 + ... + 24324308.

It is an arithmetic number, because the mean of its divisors is an integer number (2211664).

Almost surely, 2^413513100 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413513100, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (955438848).

413513100 is an abundant number, since it is smaller than the sum of its proper divisors (1497364596).

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

413513100 is a wasteful number, since it uses less digits than its factorization.

413513100 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 77 (or 58 counting only the distinct ones).

The product of its (nonzero) digits is 180, while the sum is 18.

The square root of 413513100 is about 20335.0215146186. The cubic root of 413513100 is about 745.0116959862.

Adding to 413513100 its reverse (1315314), we get a palindrome (414828414).

The spelling of 413513100 in words is "four hundred thirteen million, five hundred thirteen thousand, one hundred".