413976684737889 has 343 divisors, whose sum is σ = 784470971270743. Its totient is φ = 218361328213392.

The previous prime is 413976684737821. The next prime is 413976684738037. The reversal of 413976684737889 is 988737486679314.

The square root of 413976684737889 is 20346417.

The cubic root of 413976684737889 is 74529.

It is a perfect power (a square, a cube, a 6-th power), and thus also a powerful number.

413976684737889 is a `hidden beast` number, since 4 + 1 + 3 + 9 + 7 + 6 + 68 + 473 + 78 + 8 + 9 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 355176804438225 + 58799880299664 = 18846135^2 + 7668108^2 .

It is a tau number, because it is divible by the number of its divisors (343).

It is not a de Polignac number, because 413976684737889 - 2¹¹ = 413976684735841 is a prime.

It is a Duffinian number.

It is a junction number, because it is equal to n+sod(n) for n = 413976684737799 and 413976684737808.

It is not an unprimeable number, because it can be changed into a prime (413976684737809) by changing a digit.

It is a polite number, since it can be written in 342 ways as a sum of consecutive naturals, for example, 31844360364447 + ... + 31844360364459.

Almost surely, 2^{413976684737889} is an apocalyptic number.

413976684737889 is a gapful number since it is divisible by the number (49) formed by its first and last digit.

413976684737889 is the 20346417-th square number.

413976684737889 is the 10173209-th centered octagonal number.

It is an amenable number.

413976684737889 is a deficient number, since it is larger than the sum of its proper divisors (370494286532854).

413976684737889 is an frugal number, since it uses more digits than its factorization.

413976684737889 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 138 (or 23 counting only the distinct ones).

The product of its digits is 73741860864, while the sum is 90.

The spelling of 413976684737889 in words is "four hundred thirteen trillion, nine hundred seventy-six billion, six hundred eighty-four million, seven hundred thirty-seven thousand, eight hundred eighty-nine".