Has it been conjectured that all $k$-multiperfect numbers are multiples of $k$?
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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 ?
number-theory perfect-numbers
asked Dec 3 '18 at 22:49
Sylvain JulienSylvain Julien
1,127918
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add a comment |
$begingroup$
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 ?
number-theory perfect-numbers
asked Dec 3 '18 at 22:49
Sylvain JulienSylvain Julien
1,127918
$endgroup$
1
$begingroup$
Wikipedia says it's an open question whether $k$-perfect numbers are divisible by $k!$.
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– Qiaochu Yuan
Dec 3 '18 at 23:29
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@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.
$endgroup$
– Jose Arnaldo Bebita Dris
Dec 19 '18 at 5:35
add a comment |
$begingroup$
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 ?
number-theory perfect-numbers
asked Dec 3 '18 at 22:49
Sylvain JulienSylvain Julien
1,127918
$endgroup$
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 ?
number-theory perfect-numbers
number-theory perfect-numbers
asked Dec 3 '18 at 22:49
Sylvain JulienSylvain Julien
1,127918
asked Dec 3 '18 at 22:49
Sylvain JulienSylvain Julien
1,127918
asked Dec 3 '18 at 22:49
Sylvain JulienSylvain Julien
1,127918
asked Dec 3 '18 at 22:49
Sylvain JulienSylvain Julien
1,127918
asked Dec 3 '18 at 22:49
Sylvain JulienSylvain Julien
1,127918
1,127918
1
$begingroup$
Wikipedia says it's an open question whether $k$-perfect numbers are divisible by $k!$.
$endgroup$
– Qiaochu Yuan
Dec 3 '18 at 23:29
$begingroup$
@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.
$endgroup$
– Jose Arnaldo Bebita Dris
Dec 19 '18 at 5:35
add a comment |
1
$begingroup$
Wikipedia says it's an open question whether $k$-perfect numbers are divisible by $k!$.
$endgroup$
– Qiaochu Yuan
Dec 3 '18 at 23:29
$begingroup$
@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.
$endgroup$
– Jose Arnaldo Bebita Dris
Dec 19 '18 at 5:35
1
1
$begingroup$
Wikipedia says it's an open question whether $k$-perfect numbers are divisible by $k!$.
$endgroup$
– Qiaochu Yuan
Dec 3 '18 at 23:29
$begingroup$
Wikipedia says it's an open question whether $k$-perfect numbers are divisible by $k!$.
$endgroup$
– Qiaochu Yuan
Dec 3 '18 at 23:29
$begingroup$
@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.
$endgroup$
– Jose Arnaldo Bebita Dris
Dec 19 '18 at 5:35
$begingroup$
@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.
$endgroup$
– Jose Arnaldo Bebita Dris
Dec 19 '18 at 5:35
add a comment |
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$begingroup$
Wikipedia says it's an open question whether $k$-perfect numbers are divisible by $k!$.
$endgroup$
– Qiaochu Yuan
Dec 3 '18 at 23:29
$begingroup$
@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.
$endgroup$
– Jose Arnaldo Bebita Dris
Dec 19 '18 at 5:35