Hello everyone!

I came across a strange question today. Consider a number say 10, we will try to express it as a sum of positive integers say

$10 = \underbrace{1+1+1+\cdots + 1}_{\text{ten 1's}} = 2 + 4 + 4 = 2 + 3 + 5 = \cdots$

We find the maximum possible lowest common multiple of these numbers and call it $$S_{10}$$, so $$S_{10} = 2\times3\times5=30$$.

Other examples are $$S_{7} = 3\times4=12, S_{8} = 3\times5=15$$.

Is there a way to find $$S_{n}$$ for all positive integers $$n$$?

Note by Keshav Tiwari
2 years, 1 month ago

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Sort by:

- 2 years, 1 month ago

Yes there is a way.

What have you tried?

Staff - 2 years, 1 month ago

Not much ,I did it by hit and trial for small numbers( as most questions asked only about them) .I have no idea on how to proceed with large numbers.

- 2 years, 1 month ago

Try smoothing an inequality.

Staff - 2 years, 1 month ago