math.CO/0409509 number 34

[rwst]

What is the conjecture

$$ \sigma(d(n^3))=d(\sigma(n^2))\implies n\equiv1\bmod24. $$

Prerequisites needed

Status: closed

Choose either option

• I plan on adding this conjecture to the repository
• This issue is up for grabs: I would like to see this conjecture added by somebody else

[rwst]

Comment in https://oeis.org/A063797 : Not all $a(n)$ are 1 mod 24. First counterexample is 5036684. But for a prime $p$, with sigma( $p^4$ ) squarefree and omega(sigma( $p^4$ )==3, $p^2$ is in $a(n)$. For these primes (as for all primes > 3), $p^2$ = 1 mod 24. - Lambert Herrgesell (lambert.herrgesell(AT)googlemail.com), Jan 08 2007, edited by Robert Israel, Oct 22 2018.

So, this is refuted and explained at the same time.