New Number Theory Conjecture [on hold]

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I have accidentally created a conjecture in number theory. In an attempt to disprove the existence of odd perfect numbers I noticed a pattern and formulated an equation. If this equation I created can be proven to be mathematically sound, then I will have successfully disproved the existence of odd perfect numbers.



My conjecture states: N = PN[σ1(N)/d(N)]



Where,



  • N is a perfect number (generated by P)

  • PN is the Mersenne Prime exponent (2^(PN-1)(2^(PN) - 1))

  • σ1(N) is the summation of the divisors of N (including 1 and N)

  • d(N) is the number of divisors of N (including 1 and N)

For example:



N = 28



P28 = 3 | 2^(3-1)(2^(3) - 1) = 28



σ1(28) = 1 + 2 + 4 + 7 + 14 + 28 = 56



d(28) = 6



28 = 3[56/6] or 28 = 28



I have tested my equation for every known perfect number and it has always been correct. My only problem now is that I am clueless on how to prove that my conjecture works for all perfect numbers. Is there any way to prove this relationship?




number-theory prime-numbers divisor-sum perfect-numbers mersenne-numbers




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put on hold as off-topic by Elliot G, Morgan Rodgers, gammatester, Hans Lundmark, David G. Stork 6 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Elliot G, Morgan Rodgers, gammatester, Hans Lundmark, David G. Stork
If this question can be reworded to fit the rules in the help center, please edit the question.












  • This could be interesting but I can’t follow it. Can you show a couple examples of all these terms and the result?
    – Randall
    6 hours ago










  • For the known perfect number $N=28$, $fracσ1(N)d(N)=frac1+2+4+7+14+286=9frac13$. Does this fit into your pattern?
    – James Arathoon
    6 hours ago











  • For perfect numbers $sigma_1(N)=2N$, so the equation is really $d(N)=2P_N$, this should be an easy exercise. Of course the question should clear up that you consider only even perfect numbers here.
    – Arnaud Mortier
    3 hours ago











  • (continued) since you talk about Mersenne primes, which are known to be in $1$-$1$ correspondence with perfect numbers.
    – Arnaud Mortier
    3 hours ago















up vote
1
down vote

favorite
4












I have accidentally created a conjecture in number theory. In an attempt to disprove the existence of odd perfect numbers I noticed a pattern and formulated an equation. If this equation I created can be proven to be mathematically sound, then I will have successfully disproved the existence of odd perfect numbers.



My conjecture states: N = PN[σ1(N)/d(N)]



Where,



  • N is a perfect number (generated by P)

  • PN is the Mersenne Prime exponent (2^(PN-1)(2^(PN) - 1))

  • σ1(N) is the summation of the divisors of N (including 1 and N)

  • d(N) is the number of divisors of N (including 1 and N)

For example:



N = 28



P28 = 3 | 2^(3-1)(2^(3) - 1) = 28



σ1(28) = 1 + 2 + 4 + 7 + 14 + 28 = 56



d(28) = 6



28 = 3[56/6] or 28 = 28



I have tested my equation for every known perfect number and it has always been correct. My only problem now is that I am clueless on how to prove that my conjecture works for all perfect numbers. Is there any way to prove this relationship?




number-theory prime-numbers divisor-sum perfect-numbers mersenne-numbers




share|cite|improve this question













put on hold as off-topic by Elliot G, Morgan Rodgers, gammatester, Hans Lundmark, David G. Stork 6 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Elliot G, Morgan Rodgers, gammatester, Hans Lundmark, David G. Stork
If this question can be reworded to fit the rules in the help center, please edit the question.












  • This could be interesting but I can’t follow it. Can you show a couple examples of all these terms and the result?
    – Randall
    6 hours ago










  • For the known perfect number $N=28$, $fracσ1(N)d(N)=frac1+2+4+7+14+286=9frac13$. Does this fit into your pattern?
    – James Arathoon
    6 hours ago











  • For perfect numbers $sigma_1(N)=2N$, so the equation is really $d(N)=2P_N$, this should be an easy exercise. Of course the question should clear up that you consider only even perfect numbers here.
    – Arnaud Mortier
    3 hours ago











  • (continued) since you talk about Mersenne primes, which are known to be in $1$-$1$ correspondence with perfect numbers.
    – Arnaud Mortier
    3 hours ago













up vote
1
down vote

favorite
4









up vote
1
down vote

favorite
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4





I have accidentally created a conjecture in number theory. In an attempt to disprove the existence of odd perfect numbers I noticed a pattern and formulated an equation. If this equation I created can be proven to be mathematically sound, then I will have successfully disproved the existence of odd perfect numbers.



My conjecture states: N = PN[σ1(N)/d(N)]



Where,



  • N is a perfect number (generated by P)

  • PN is the Mersenne Prime exponent (2^(PN-1)(2^(PN) - 1))

  • σ1(N) is the summation of the divisors of N (including 1 and N)

  • d(N) is the number of divisors of N (including 1 and N)

For example:



N = 28



P28 = 3 | 2^(3-1)(2^(3) - 1) = 28



σ1(28) = 1 + 2 + 4 + 7 + 14 + 28 = 56



d(28) = 6



28 = 3[56/6] or 28 = 28



I have tested my equation for every known perfect number and it has always been correct. My only problem now is that I am clueless on how to prove that my conjecture works for all perfect numbers. Is there any way to prove this relationship?




number-theory prime-numbers divisor-sum perfect-numbers mersenne-numbers




share|cite|improve this question













I have accidentally created a conjecture in number theory. In an attempt to disprove the existence of odd perfect numbers I noticed a pattern and formulated an equation. If this equation I created can be proven to be mathematically sound, then I will have successfully disproved the existence of odd perfect numbers.



My conjecture states: N = PN[σ1(N)/d(N)]



Where,



  • N is a perfect number (generated by P)

  • PN is the Mersenne Prime exponent (2^(PN-1)(2^(PN) - 1))

  • σ1(N) is the summation of the divisors of N (including 1 and N)

  • d(N) is the number of divisors of N (including 1 and N)

For example:



N = 28



P28 = 3 | 2^(3-1)(2^(3) - 1) = 28



σ1(28) = 1 + 2 + 4 + 7 + 14 + 28 = 56



d(28) = 6



28 = 3[56/6] or 28 = 28



I have tested my equation for every known perfect number and it has always been correct. My only problem now is that I am clueless on how to prove that my conjecture works for all perfect numbers. Is there any way to prove this relationship?





number-theory prime-numbers divisor-sum perfect-numbers mersenne-numbers





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited 5 hours ago
























asked 6 hours ago









Maxwell Schaffer

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put on hold as off-topic by Elliot G, Morgan Rodgers, gammatester, Hans Lundmark, David G. Stork 6 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Elliot G, Morgan Rodgers, gammatester, Hans Lundmark, David G. Stork
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Elliot G, Morgan Rodgers, gammatester, Hans Lundmark, David G. Stork 6 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Elliot G, Morgan Rodgers, gammatester, Hans Lundmark, David G. Stork
If this question can be reworded to fit the rules in the help center, please edit the question.











  • This could be interesting but I can’t follow it. Can you show a couple examples of all these terms and the result?
    – Randall
    6 hours ago










  • For the known perfect number $N=28$, $fracσ1(N)d(N)=frac1+2+4+7+14+286=9frac13$. Does this fit into your pattern?
    – James Arathoon
    6 hours ago











  • For perfect numbers $sigma_1(N)=2N$, so the equation is really $d(N)=2P_N$, this should be an easy exercise. Of course the question should clear up that you consider only even perfect numbers here.
    – Arnaud Mortier
    3 hours ago











  • (continued) since you talk about Mersenne primes, which are known to be in $1$-$1$ correspondence with perfect numbers.
    – Arnaud Mortier
    3 hours ago

















  • This could be interesting but I can’t follow it. Can you show a couple examples of all these terms and the result?
    – Randall
    6 hours ago










  • For the known perfect number $N=28$, $fracσ1(N)d(N)=frac1+2+4+7+14+286=9frac13$. Does this fit into your pattern?
    – James Arathoon
    6 hours ago











  • For perfect numbers $sigma_1(N)=2N$, so the equation is really $d(N)=2P_N$, this should be an easy exercise. Of course the question should clear up that you consider only even perfect numbers here.
    – Arnaud Mortier
    3 hours ago











  • (continued) since you talk about Mersenne primes, which are known to be in $1$-$1$ correspondence with perfect numbers.
    – Arnaud Mortier
    3 hours ago
















This could be interesting but I can’t follow it. Can you show a couple examples of all these terms and the result?
– Randall
6 hours ago




This could be interesting but I can’t follow it. Can you show a couple examples of all these terms and the result?
– Randall
6 hours ago












For the known perfect number $N=28$, $fracσ1(N)d(N)=frac1+2+4+7+14+286=9frac13$. Does this fit into your pattern?
– James Arathoon
6 hours ago





For the known perfect number $N=28$, $fracσ1(N)d(N)=frac1+2+4+7+14+286=9frac13$. Does this fit into your pattern?
– James Arathoon
6 hours ago













For perfect numbers $sigma_1(N)=2N$, so the equation is really $d(N)=2P_N$, this should be an easy exercise. Of course the question should clear up that you consider only even perfect numbers here.
– Arnaud Mortier
3 hours ago





For perfect numbers $sigma_1(N)=2N$, so the equation is really $d(N)=2P_N$, this should be an easy exercise. Of course the question should clear up that you consider only even perfect numbers here.
– Arnaud Mortier
3 hours ago













(continued) since you talk about Mersenne primes, which are known to be in $1$-$1$ correspondence with perfect numbers.
– Arnaud Mortier
3 hours ago





(continued) since you talk about Mersenne primes, which are known to be in $1$-$1$ correspondence with perfect numbers.
– Arnaud Mortier
3 hours ago
















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