40961

40961 is an integer. It is an odd number, as it is not divisible by 2. Its prime factorization is 13 * 3151. 3151 is a prime number. 40961 can be expressed as the sum of two squares: 150^2 + 131^2. It is also the sum of three cubes in two different ways: 34^3 + 12^3 + (-11)^3 and 32^3 + 22^3 + (-16)^3. In base 10, 40961 is a palindromic number. It is also a happy number, meaning that if you repeatedly replace the number by the sum of the squares of its digits, you will eventually reach 1. The sequence is 40961 -> 4^2 + 0^2 + 9^2 + 6^2 + 1^2 = 16 + 0 + 81 + 36 + 1 = 134 -> 1^2 + 3^2 + 4^2 = 1 + 9 + 16 = 26 -> 2^2 + 6^2 = 4 + 36 = 40 -> 4^2 + 0^2 = 16 -> 1^2 + 6^2 = 1 + 36 = 37 -> 3^2 + 7^2 = 9 + 49 = 58 -> 5^2 + 8^2 = 25 + 64 = 89 -> 8^2 + 9^2 = 64 + 81 = 145 -> 1^2 + 4^2 + 5^2 = 1 + 16 + 25 = 42 -> 4^2 + 2^2 = 16 + 4 = 20 -> 2^2 + 0^2 = 4 -> 4^2 = 16 -> 1^2 + 6^2 = 37... wait, this is not leading to 1. Rechecking the definition, a happy number is one that eventually reaches 1. If it enters a cycle that does not include 1, it is an unhappy number. Let's recompute: 40961 -> 134 -> 26 -> 40 -> 16 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16. This sequence enters the cycle 16, 37, 58, 89, 145, 42, 20, 4. Therefore, 40961 is an unhappy number.