Problem 805

[castrate]

How is s(n) defined when n has only 1 digit? Is it n itself?
So is N(1) just equal to 1 since s(1)=1 is the smallest number satisfying s(n)=1*n?

[neverforget]

For single digit $n$, $s(n)=n$.

And yes, $N(1)=1$.

[radeye]

In problem 805, the $T(M)$ uses an upper-case $M$, while the later reference to the function parameter uses a lower-case $m$. Indeed this whole problem has a really interesting combination of upper- and lower-case identifiers.

[bruce_love]

Thanks for that radeye - it has been fixed. Changing the later reference $m$ to $M$.

[Dusterbraut]

Sorry,

I don't understand English very well.
My question is:

What are "... all ordered pairs of coprime positive integers not exceeding $M$"?

Do you mean all pairs (u,v) with 1 <= u < v <= M with gcd (u,v) = 1 ?

Thanks a lot for answering my stupid little question.

[neverforget]

There's no restriction that $u<v$.
It's all $1\leq u\leq M$ and $1\leq v\leq M$ where $\gcd(u,v)=1$