Turns out that indeed, more people picked 17 than any other number: 12 out of 68, or 17.6%. The runner-up was 7, with 8 out of 68, or 11.8%. Most of the other numbers scored 1 or 3 votes.
Since the average number of votes for each number, if the 68 people had truly picked at random, would have been 3.4 if 1 and 20 were counted, or 3.8 if they weren't, having 3 be the most common number of votes is consistent with that. Interesting, then, that 7 and 17 scored so many more votes.