Sigma_2(n)
y.kohmoto
zbi74583 at boat.zero.ad.jp
Fri Mar 26 07:53:38 CET 2004
Hello, seqfans.
I searched small solutions of the following equations. x<100000.
Sigma_2(x)=Sigma_2(y)=x^2+y^2
Sigma_2(x)=k*x^2
Where Sigma_2(n) means the sum of square of divisors of n.
But if my software is correct, no solution exists.
Is it possible to prove it? Or, does a solution exist?
I knew the following sequence doesn't exist on OEIS.
a(n) : 1,4,9,16,25,36,49,50,64,81,100,117,
Sigma_2(n)/Sigma(n)=integer
example :
Sigma_2(4)/Sigma(4)=(1+4+16)/(1+2+4)=3 , so 4 appears on a(n).
It is easy but interesting.
I will try to calculate Sigma_i(n)/Sigma_j(n) on several pairs {i,j}.
Yasutoshi
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