Non-trivial divisors Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Are there any non-trivial rational integers in the $p$-adic closure of $1,q,q^2,q^3,…$?The number of positive integers less than 1000 with an odd number of divisorsThe rigorousness of this proof about greatest common divisors.Prove that among any 12 consecutive positive integers there is at least one which is smaller than the sum of its proper divisorsDo all members of this sequence have $8$ divisors?Proper Divisors / Number TheoryConstruct a non trivial homomorphism $mathbb Z_14 tomathbb Z_21$Smallest integer that is divisible by 90 and has exactly 90 distinct positive divisorsInteger divisors of an integerFind all natural numbers $n$, such that polynomial $n^7+n^6+n^5+1$ would have exactly 3 divisors.
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Non-trivial divisors
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Are there any non-trivial rational integers in the $p$-adic closure of $1,q,q^2,q^3,…$?The number of positive integers less than 1000 with an odd number of divisorsThe rigorousness of this proof about greatest common divisors.Prove that among any 12 consecutive positive integers there is at least one which is smaller than the sum of its proper divisorsDo all members of this sequence have $8$ divisors?Proper Divisors / Number TheoryConstruct a non trivial homomorphism $mathbb Z_14 tomathbb Z_21$Smallest integer that is divisible by 90 and has exactly 90 distinct positive divisorsInteger divisors of an integerFind all natural numbers $n$, such that polynomial $n^7+n^6+n^5+1$ would have exactly 3 divisors.
$begingroup$
I want to find out the number of integers whose biggest non-trivial divisor is exactly $k$ times the smallest non-trivial divisor of that integer.
My thoughts are, that the smallest divisor $n$ has to be prime, otherwise the divisor would have smaller divisors, which would divide the larger integer too.
Also the biggest divisor would be $kn$. Also I believe that the integers have to be in the form $mkn$, and then I would have to exclude some of these integers because the property does not hold, but i am not sure how to prove that.
number-theory elementary-number-theory divisibility
asked Apr 2 at 0:43
M-S-RM-S-R
505
$endgroup$
add a comment |
$begingroup$
I want to find out the number of integers whose biggest non-trivial divisor is exactly $k$ times the smallest non-trivial divisor of that integer.
My thoughts are, that the smallest divisor $n$ has to be prime, otherwise the divisor would have smaller divisors, which would divide the larger integer too.
Also the biggest divisor would be $kn$. Also I believe that the integers have to be in the form $mkn$, and then I would have to exclude some of these integers because the property does not hold, but i am not sure how to prove that.
number-theory elementary-number-theory divisibility
asked Apr 2 at 0:43
M-S-RM-S-R
505
$endgroup$
2
$begingroup$
Note that every number (with at least 1 non-trivial divisor) is the product of their smallest and largest non-trivial divisors. This means your number is $kn^2$ for $n$ prime and $k$ having no prime factors less than $n$.
$endgroup$
– Don Thousand
Apr 2 at 0:46
$begingroup$
so the smallest non-trivial divisor has to be prime, and then I get the integer $kn^2$, but the relationship to the number of such integers still eludes me
$endgroup$
– M-S-R
Apr 2 at 0:59
add a comment |
$begingroup$
I want to find out the number of integers whose biggest non-trivial divisor is exactly $k$ times the smallest non-trivial divisor of that integer.
My thoughts are, that the smallest divisor $n$ has to be prime, otherwise the divisor would have smaller divisors, which would divide the larger integer too.
Also the biggest divisor would be $kn$. Also I believe that the integers have to be in the form $mkn$, and then I would have to exclude some of these integers because the property does not hold, but i am not sure how to prove that.
number-theory elementary-number-theory divisibility
asked Apr 2 at 0:43
M-S-RM-S-R
505
$endgroup$
I want to find out the number of integers whose biggest non-trivial divisor is exactly $k$ times the smallest non-trivial divisor of that integer.
My thoughts are, that the smallest divisor $n$ has to be prime, otherwise the divisor would have smaller divisors, which would divide the larger integer too.
Also the biggest divisor would be $kn$. Also I believe that the integers have to be in the form $mkn$, and then I would have to exclude some of these integers because the property does not hold, but i am not sure how to prove that.
number-theory elementary-number-theory divisibility
number-theory elementary-number-theory divisibility
asked Apr 2 at 0:43
M-S-RM-S-R
505
asked Apr 2 at 0:43
M-S-RM-S-R
505
asked Apr 2 at 0:43
M-S-RM-S-R
505
asked Apr 2 at 0:43
M-S-RM-S-R
505
asked Apr 2 at 0:43
M-S-RM-S-R
505
505
2
$begingroup$
Note that every number (with at least 1 non-trivial divisor) is the product of their smallest and largest non-trivial divisors. This means your number is $kn^2$ for $n$ prime and $k$ having no prime factors less than $n$.
$endgroup$
– Don Thousand
Apr 2 at 0:46
$begingroup$
so the smallest non-trivial divisor has to be prime, and then I get the integer $kn^2$, but the relationship to the number of such integers still eludes me
$endgroup$
– M-S-R
Apr 2 at 0:59
add a comment |
2
$begingroup$
Note that every number (with at least 1 non-trivial divisor) is the product of their smallest and largest non-trivial divisors. This means your number is $kn^2$ for $n$ prime and $k$ having no prime factors less than $n$.
$endgroup$
– Don Thousand
Apr 2 at 0:46
$begingroup$
so the smallest non-trivial divisor has to be prime, and then I get the integer $kn^2$, but the relationship to the number of such integers still eludes me
$endgroup$
– M-S-R
Apr 2 at 0:59
2
2
$begingroup$
Note that every number (with at least 1 non-trivial divisor) is the product of their smallest and largest non-trivial divisors. This means your number is $kn^2$ for $n$ prime and $k$ having no prime factors less than $n$.
$endgroup$
– Don Thousand
Apr 2 at 0:46
$begingroup$
Note that every number (with at least 1 non-trivial divisor) is the product of their smallest and largest non-trivial divisors. This means your number is $kn^2$ for $n$ prime and $k$ having no prime factors less than $n$.
$endgroup$
– Don Thousand
Apr 2 at 0:46
$begingroup$
so the smallest non-trivial divisor has to be prime, and then I get the integer $kn^2$, but the relationship to the number of such integers still eludes me
$endgroup$
– M-S-R
Apr 2 at 0:59
$begingroup$
so the smallest non-trivial divisor has to be prime, and then I get the integer $kn^2$, but the relationship to the number of such integers still eludes me
$endgroup$
– M-S-R
Apr 2 at 0:59
add a comment |
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2
$begingroup$
Note that every number (with at least 1 non-trivial divisor) is the product of their smallest and largest non-trivial divisors. This means your number is $kn^2$ for $n$ prime and $k$ having no prime factors less than $n$.
$endgroup$
– Don Thousand
Apr 2 at 0:46
$begingroup$
so the smallest non-trivial divisor has to be prime, and then I get the integer $kn^2$, but the relationship to the number of such integers still eludes me
$endgroup$
– M-S-R
Apr 2 at 0:59