Blog Post # 92: Ramanujan Number Neighbourhood

1729 has a special place in the Number world thanks to the genius of Ramanujan

Let's explore the neighbourhood of 1729 as I am sure some of those will exhibit special attributes as well being closer to GOD Number!

1728 is in Focus in this Blog

- For starters 1728 is multiple of two cubes - 3 ^ 3 x 4 ^ 3 (27 x 64)

- Now take the two factors (27 and 64) - Add both and you get 91. 91 multiplied with 19 (reverse) gives back Ramanujan Number!

- 1728 is also difference of two perfect squares - 1764 - 36. Now add the digits of 1764 in pairs (17 + 64 = 81) and subtract 36. The result is 45 which is sum of the digit pairs of 1728 (17 + 28)!

- One of the anagrams of 1728 is 2187 which 3 ^ 7 (refer to Blog No.91)

- Multiply 18 and 72 (digit pairs of 1728) and you get another perfect square - 1296

As always the best is reserved for the last

Sum of the cubes of its digits - 1 ^ 3 + 7 ^ 3 + 2 ^ 3 + 8 ^ 3 = 864 which is exactly half of 1728. Very few numbers exhibit this

The neighbourhood of Ramanujan number looks amazing and watch out this space for more!

Blog Post No.91 - The magical number 2187

Another number that provides some fascinating insights on how digits 2, 3, 7 combine and create magic

- 2187 is 3 ^ 7
- 3 x 7 is 21 which are the first two digits
- First digit (2) ^ 3 (sum of first 2 digits) is 3rd digit - 8
- First 2 digits (21) divided by sum of first 2 digits is 4th digit - 7

And for few more medium complex ones,

- 218 + 7 is 225
      - Insert 0 as the 2nd digit makes it 2025 which is 45 ^ 2 and 45 in turn is 27 + 18 or 28 + 17 (sum of digits)
      - Insert 0 as the 3rd digit makes it 2205 which is 441 x 5 (3 ^ 2 x 7 ^ 2 x (3+7)/2)

- 2187 is product of its own digits - 27 x 81

- 2187 can also be written as - ( (7 ^ 3) - (7+3) ^ 2 ) x 3 ^ 2

And best is reserved for the last

21 + 87 is 108 and 87 - 21 is 66. Multiplication of 108 x 66 gives 7128 which is an anagram of 2187