[seqfan] Re: 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
Jakob Schulz
bruderjakob17 at gmail.com
Fri Mar 11 16:33:03 CET 2022
Dear Thomas,
While I cannot answer any of your questions, I think that D(n) is already
in the OEIS as A083346(n). This is because s(n) = (1 - 1/p_1) + ... + (1 -
1/p_k) = k - (1/p_1 + ... + 1/p_k) = k - r(n), where r(n) is defined as in
the OEIS-entry.
Best,
Jakob
Am Fr., 11. März 2022 um 08:29 Uhr schrieb Thomas Scheuerle via SeqFan <
seqfan at list.seqfan.eu>:
> Hi,
>
> 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
>
> Thomas
>
>
>
>
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