Starter Set for N/S HO

The number 26247 is a positive integer that can be expressed as the product of its prime factors. It is divisible by 7, and when divided by 7, the result is 3749. The number 26247 can also be written as the sum of two perfect squares, with one square being 169 and the other being 25.

Interestingly, 26247 is a repdigit in base 9, meaning that all of its digits in base 9 are the same. In base 9, 26247 is represented as 2222. Additionally, 26247 is a palindromic number, meaning that it reads the same forwards and backwards.

Another notable property of 26247 is that it is a Harshad number. A Harshad number is an integer that is divisible by the sum of its digits. In the case of 26247, the sum of its digits is 2 + 6 + 2 + 4 + 7 = 21, and 26247 is indeed divisible by 21.

Furthermore, 26247 is a highly composite number, meaning that it has more divisors than any smaller positive integer. The divisors of 26247 are 1, 3, 7, 9, 21, 27, 39, 63, 117, 169, 189, 247, 351, 378, 507, 729, 837, 1116, 1701, 2511, 3749, 5022, 7533, 10044, 15066, and 26247.

Interestingly, 26247 is also a Smith number, which is a composite number for which the sum of its digits is equal to the sum of the digits of its prime factors. In the case of 26247, the sum of its digits is 2 + 6 + 2 + 4 + 7 = 21, and the sum of the digits of its prime factors (3, 7, and 3749) is also 21.

In conclusion, the number 26247 exhibits several intriguing mathematical properties, including being a product of prime factors, a sum of perfect squares, a repdigit in base 9, a palindromic number, a Harshad number, a highly composite number, and a Smith number. These diverse characteristics make 26247 an interesting and noteworthy integer worth exploring further.

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