# Has it been conjectured that all $k$-multiperfect numbers are multiples of $k$?

A quick glance at the list of the first $$k$$ -multiperfect numbers for small $$k$$ makes me think that all $$k$$ -multiperfect numbers are multiples of $$k$$ , which is a generalization of the famous "no odd perfect number" conjecture. Has this conjecture appeared so far ? If yes, what are the results towards it so far ?

• Wikipedia says it's an open question whether $k$-perfect numbers are divisible by $k!$. – Qiaochu Yuan Dec 3 '18 at 23:29
• @QiaochuYuan: By chance, do you happen to know of any reference (in the literature) to the conjecture that $k$-perfect numbers must be divisible by $k!$? I checked the Wikipedia page and there is none there. – Jose Arnaldo Bebita-Dris Dec 19 '18 at 5:35