[seqfan] Let p_1 .. p_k be prime divisors of n counted with multiplicity, then consider the rational number (p_1-1)/p_1 + (p_2-1)/p_2 + ... (p_k-1)/p_k

Thomas Scheuerle ts181 at mail.ru
Thu Mar 10 20:51:14 CET 2022


If we see the numerators and the denominators of 
s(n) = (p_1-1)/p_1 + (p_2-1)/p_2 + ... (p_k-1)/p_k  
as integersequences N(n), D(n)
then we will observe mysterious lines and other more 
complicated looking structures,if we plot N(n) against D(n) in a X,Y scatter plot.
This fact was enough motivation for me,
but now I am asking my self what other interesting properties
or maybe even applications could such a sequence have.

Maybe someone out there has some ideas what properties should be checked
or what properties could be possibly expected from such a sequence ?
(I should better say sequences as we have numerator and denominator here.)

best rgeards


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