413105625 has 45 divisors (see below), whose sum is σ = 748408089. Its totient is φ = 219510000.

The previous prime is 413105611. The next prime is 413105677. The reversal of 413105625 is 526501314.

The square root of 413105625 is 20325.

It is a perfect power (a square), and thus also a powerful number.

413105625 is a `hidden beast` number, since 4 + 1 + 31 + 0 + 5 + 625 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 32387481 + 380718144 = 5691^2 + 19512^2 .

It is a tau number, because it is divible by the number of its divisors (45).

It is not a de Polignac number, because 413105625 - 2²³ = 404717017 is a prime.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 44 ways as a sum of consecutive naturals, for example, 1524240 + ... + 1524510.

Almost surely, 2^413105625 is an apocalyptic number.

413105625 is a gapful number since it is divisible by the number (45) formed by its first and last digit.

413105625 is the 20325-th square number.

413105625 is the 10163-rd centered octagonal number.

It is an amenable number.

413105625 is a deficient number, since it is larger than the sum of its proper divisors (335302464).

413105625 is an frugal number, since it uses more digits than its factorization.

413105625 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 568 (or 279 counting only the distinct ones).

The product of its (nonzero) digits is 3600, while the sum is 27.

The cubic root of 413105625 is about 744.7669045402.

Multiplying 413105625 by its product of nonzero digits (3600), we get a square (1487180250000 = 1219500²).

Adding to 413105625 its reverse (526501314), we get a palindrome (939606939).

The spelling of 413105625 in words is "four hundred thirteen million, one hundred five thousand, six hundred twenty-five".