For p = prime(n), the total of the absolute value of the differences of the inverses of the numbers 1..p-1 (mod p).
0, 1, 5, 11, 35, 37, 93, 103, 195, 293, 287, 365, 501, 551, 807, 985, 1231, 845, 1447, 1715, 1417, 2235, 2615, 2793, 2901, 3321, 3579, 4399, 3485, 3989, 4595, 5491, 6373, 6395, 8125, 7679, 8229, 8599, 10147, 10381, 11763, 9937, 12375, 10345, 14113, 13715
1
Somewhat surprisingly, these numbers have a fairly regular pattern. The value of a(n) is about prime(n)^2/3. The movie link below presents the inverses in a much better way than the graph in A124223.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
T. D. Noe, Movie of 100 frames of the inverses (mod p)
(Mma) Table[s = Table[PowerMod[b, -1, Prime[m]], {b, Prime[m] - 1}]; Plus @@ Abs[Differences[s]], {m, 100}]
Cf. A124223 (inverses of the numbers 1..p-1 (mod p)).
nonn,nice
T. D. Noe, Aug 21 2014