Dear Math Fun: The sequence https://oeis.org/A257007 just arose in two possibly different contexts. The sequence appears to be the same as the function Phi(n) in Theorem 4 of this paper: P. Kleban and A. Özlük. A farey fraction spin chain. Communications in mathematical physics, 203(3):635-647, 1999. Also http://arxiv.org/pdf/cond-mat/9808182.pdf. I discovered this when I was looking at a recent thesis: M. P. Technau, The Calkin-Wilf Tree and a Trace Condition, Master's Thesis, Julius-Maximilian’s University of Würzburg, Faculty for Mathematics and Computer Science, 2015; http://www.mathematik.uni-wuerzburg.de/~steuding/technau.pdf On page 14 there is a triangle of numbers. The first column of the triangle seems to match A257007, and the row sums in the triangle are twice the first column. I created three new sequences, A264597, A264598, A264599 from this paper. It would be nice to know for certain that it is the same sequence (A257007) in all three cases! Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com