# [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

Thomas Scheuerle ts181 at mail.ru
Fri Mar 11 19:23:38 CET 2022

```Hi,

I want to thank you all for your input.
I was to quick with writing this e-mail and did not write that
I already suspected the denominator to be A083346, thank you for confirming this Jakob.
What I also know yet is that we reach integer values
for all values of A072873.

if n is a product of p1^e1*..*pm^em then we get
(e1*(p1-1)/p1)+..+(em*(pm-1)/pm) which is essentially A001414(n)-(A083345(n)/A083346(n)).

For the integer case where n is from A083346
we know that n is of the form: p1^p1^e1*..*pm^pm^em
then we get p1^e1-p1^(e1-1)+..+pm^em-pm^(em-1) may be a interesting sequence on its own:
0,1,2,2,3,3,4,4,4,5,5,5,4,6,6,6  I will check this too further ...

Maximilian your input will help me to find further formulas as far as I can already see now.

overall I am not yet convinced of the importance of these sequences,
for example compared to A059975 which has a lot more interesting implications.

So if I find something more interesting soon, this here will not be the next in my time line
as I will probably jump unto the more interesting topic first.

thank you

best regards

Thomas

```