414448164 has 189 divisors, whose sum is σ = 1219515843. Its totient is φ = 123125184.

The previous prime is 414448157. The next prime is 414448171. The reversal of 414448164 is 461844414.

The square root of 414448164 is 20358.

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

It is an interprime number because it is at equal distance from previous prime (414448157) and next prime (414448171).

It can be written as a sum of positive squares in 4 ways, for example, as 53144100 + 361304064 = 7290^2 + 19008^2 .

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

It is an unprimeable number.

It is a polite number, since it can be written in 62 ways as a sum of consecutive naturals, for example, 14291302 + ... + 14291330.

Almost surely, 2^414448164 is an apocalyptic number.

414448164 is the 20358-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 414448164

414448164 is an abundant number, since it is smaller than the sum of its proper divisors (805067679).

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

414448164 is a wasteful number, since it uses less digits than its factorization.

414448164 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 106 (or 47 counting only the distinct ones).

The product of its digits is 49152, while the sum is 36.

The cubic root of 414448164 is about 745.5728303117.

Multiplying 414448164 by its sum of digits (36), we get a square (14920133904 = 122148²).

414448164 divided by its sum of digits (36) gives a square (11512449 = 3393²).

The spelling of 414448164 in words is "four hundred fourteen million, four hundred forty-eight thousand, one hundred sixty-four".