Emirhan 31.01.2016 19:36 Let $n$'s positive divisors sum is $T(n)$. For all $n \geq 3$'s prove that, $$(T(n))^3<n^4$$
jmerry 01.02.2016 02:04 False. $1728=12^3 > 6^4=1296$ at $n=6$. Also $343=7^3>4^4=256$ at $n=4$. It is true for $n>6$, though; only $1,2,4,6$ have the inequality reversed.