413972 has 24 divisors (see below), whose sum is σ = 823200. Its totient is φ = 180576.

The previous prime is 413951. The next prime is 413981. The reversal of 413972 is 279314.

It is a Harshad number since it is a multiple of its sum of digits (26).

It is an Ulam number.

It is a d-powerful number, because it can be written as 4⁹ + 1 + 9³ + 3⁹ + 7³ + 2¹⁷ .

It is a congruent number.

It is an unprimeable number.

413972 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 779 + ... + 1197.

It is an arithmetic number, because the mean of its divisors is an integer number (34300).

2⁴¹³⁹⁷² is an apocalyptic number.

It is an amenable number.

413972 is a deficient number, since it is larger than the sum of its proper divisors (409228).

413972 is a wasteful number, since it uses less digits than its factorization.

413972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 455 (or 453 counting only the distinct ones).

The product of its digits is 1512, while the sum is 26.

The square root of 413972 is about 643.4065588724. The cubic root of 413972 is about 74.5287188649.

The spelling of 413972 in words is "four hundred thirteen thousand, nine hundred seventy-two".