# totient valence function

Given an integer $n$, count how many integers $m$ in the set $\{n+1,n+2,\ldots n^{2}\}$ satisfy $\phi(m)=n$. This is the of $n$, usually labelled $N_{\phi}(n)$. (The only two special cases are 2 and 6, for which one has to look a little beyound $n^{2}$).

Robert Carmichael conjectured that $N_{\phi}(n)=1$ never. Two sequences in Sloane’s OEIS that list numbers with higher totient valences than preceding numbers are A007374 and A097942.

Title totient valence function TotientValenceFunction 2013-03-22 15:50:57 2013-03-22 15:50:57 CompositeFan (12809) CompositeFan (12809) 5 CompositeFan (12809) Definition msc 11A25