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 \(n\)?

## Comments

Sort by:

TopNewest@Calvin Lin – Keshav Tiwari · 1 year, 1 month ago

Log in to reply

What have you tried? – Calvin Lin Staff · 1 year, 1 month ago

Log in to reply

– Keshav Tiwari · 1 year, 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.Log in to reply

smoothing an inequality. – Calvin Lin Staff · 1 year, 1 month ago

TryLog in to reply