416681664 has 224 divisors, whose sum is σ = 1328050176. Its totient is φ = 112803840.

The previous prime is 416681651. The next prime is 416681669. The reversal of 416681664 is 466186614.

It is a tau number, because it is divible by the number of its divisors (224).

It is a super-2 number, since 2×416681664² = 347247218227617792, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (42).

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

It is not an unprimeable number, because it can be changed into a prime (416681669) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 3041404 + ... + 3041540.

Almost surely, 2^416681664 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 416681664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (664025088).

416681664 is an abundant number, since it is smaller than the sum of its proper divisors (911368512).

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

416681664 is a wasteful number, since it uses less digits than its factorization.

416681664 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 263 (or 253 counting only the distinct ones).

The product of its digits is 165888, while the sum is 42.

The square root of 416681664 is about 20412.7818780293. The cubic root of 416681664 is about 746.9097522015.

The spelling of 416681664 in words is "four hundred sixteen million, six hundred eighty-one thousand, six hundred sixty-four".