Rare Properties of Number 153

What is so special about 153?

Special Properties of Number 153:

1. Sum of Cubes of Digits:

The number 153 possesses several unique properties that make it intriguing:

• 153 is the smallest number that can be expressed as the sum of the cubes of its digits: (153 = 1^3 + 5^3 + 3^3).

2. Sum of Digits as a Perfect Square:

• The sum of the digits of 153 equals a perfect square: (1 + 5 + 3 = 9 = 3^2).

3. Sum of Aliquot Divisors:

• The sum of the aliquot divisors of 153 is also a perfect square: (1 + 3 + 9 + 17 + 51 = 81 = 9^2).
• Aliquot divisors are all divisors of a number excluding the number itself but including 1.

4. Triangular Number:

• 153 can be expressed as the sum of all integers from 1 to 17, making it the 17th triangular number.

5. Harshad Number:

• 153 is a Harshad number (also known as a Niven number) as it is divisible by the sum of its own digits: (153 / (1 + 5 + 3) = 17).

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