Some properties and applications of non-trivial divisor functions
Some properties and applications of non-trivial divisor functions
The jth divisor function $$d_j$$, which counts the ordered factorisations of a positive integer into j positive integer factors, is a very well-known multiplicative arithmetic function. However, the non-multiplicative jth non-trivial divisor function$$c_j$$, which counts the ordered factorisations of a positive integer into j factors each of which is greater …