41 modulo 42. This shows that the natural density of the friendly numbers (if it exists) is positive. Anderson and Hickerson proposed that the density should in fact be 1 (or equivalently that the density of the solitary numbers should be 0). According to the MathWorld article on Solitary Number (see References section below), this conjecture has not been resolved, although Pomerance thought at one point he had disproved it. Notes References Grime, James. A video about the number 10. Numberphile. Divisor function Integer sequences Unsolved problems in number theory