intersection of A48290 and A63986

[Max]

Note that
sum(i=1 to x) i-phi(i) = x*(x+1)/2 - sum(i=1 to x) phi(i)

So if x divides sum(i=1 to x) phi(i) and (x+1)/2 is integer (i.e., x is odd), then
x divides sum(i=1 to x) i-phi(i) as well.

Max

Jud McCranie wrote:
> I'm thinking about submitting 1, 5, 25, 249, 617, 13763, 783665, the 
> intersection of A48290 and A63986. (I recently extended both of 
> these.)   A48290 is x such that x divides the sum (i=1 to x) of phi(i).  
> A63986 such that x divides the sum (i=1 to x) of i-phi(i).  I was 
> surprised that about 1/3 of the known terms in A63986 were also in 
> A48290.  Is there any reason for this?
> 
> 
> 
>