417952 has 24 divisors (see below), whose sum is σ = 847476. Its totient is φ = 202752.

The previous prime is 417947. The next prime is 417953. The reversal of 417952 is 259714.

It is a happy number.

It can be written as a sum of positive squares in 2 ways, for example, as 404496 + 13456 = 636^2 + 116^2 .

It is a self number, because there is not a number n which added to its sum of digits gives 417952.

It is not an unprimeable number, because it can be changed into a prime (417953) by changing a digit.

417952 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 1008 + ... + 1360.

2⁴¹⁷⁹⁵² 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 417952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (423738).

417952 is an abundant number, since it is smaller than the sum of its proper divisors (429524).

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

417952 is a wasteful number, since it uses less digits than its factorization.

417952 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 400 (or 392 counting only the distinct ones).

The product of its digits is 2520, while the sum is 28.

The square root of 417952 is about 646.4920726505. The cubic root of 417952 is about 74.7668015908.

It can be divided in two parts, 417 and 952, that added together give a square (1369 = 37²).

The spelling of 417952 in words is "four hundred seventeen thousand, nine hundred fifty-two".