413921664 has 320 divisors, whose sum is σ = 1378848240. Its totient is φ = 122425344.

The previous prime is 413921659. The next prime is 413921687. The reversal of 413921664 is 466129314.

It is a super-2 number, since 2×413921664² = 342662287857057792, which contains 22 as substring.

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

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 4986967 + ... + 4987049.

Almost surely, 2^413921664 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 413921664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (689424120).

413921664 is an abundant number, since it is smaller than the sum of its proper divisors (964926576).

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

413921664 is a wasteful number, since it uses less digits than its factorization.

413921664 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 159 (or 138 counting only the distinct ones).

The product of its digits is 31104, while the sum is 36.

The square root of 413921664 is about 20345.0648561267. The cubic root of 413921664 is about 745.2569802479.

The spelling of 413921664 in words is "four hundred thirteen million, nine hundred twenty-one thousand, six hundred sixty-four".