The generating functions (gfs) for the sum of divisors of n, 2n-1, and 2n+1 are respectively inf inf inf ==== n ==== n ==== n \ n q \ (2 n - 1) q \ (2 n + 1) q (d6) [ > ------, > ------------, > ------------] / n / 2 n - 1 / 2 n + 1 ==== 1 - q ==== 1 - q ==== 1 - q n = 1 n = 1 n = 0 Check: (c7) taylor(%,q,0,9) 2 3 4 5 6 7 8 9 (d7)/T/ [q + 3 q + 4 q + 7 q + 6 q + 12 q + 8 q + 15 q + 13 q 2 3 4 5 6 7 8 + . . ., q + 4 q + 6 q + 8 q + 13 q + 12 q + 14 q + 24 q 9 2 3 4 5 6 + 18 q + . . ., 1 + 4 q + 6 q + 8 q + 13 q + 12 q + 14 q 7 8 9 + 24 q + 18 q + 20 q + . . .] What is the gf for the sum of divisors of 3n+1? Ans: http://gosper.org/3n+1.png . Should this be obvious? --rwg COMMERCIALIST MICROCLIMATES RHINOPLASTIES RELATIONSHIPS DIMESTORE DOSIMETER MOUNTAINEER ENUMERATION