How many integers n, with 2≤n≤80, is ((n-1)(n)(n+1)(n+2))/16 equal to an integer?
This list satisfies your condition:
n
1 = 6
2 = 7
3 = 8
4 = 9
5 = 14
6 = 15
7 = 16
8 = 17
9 = 22
10 = 23
11 = 24
12 = 25
13 = 30
14 = 31
15 = 32
16 = 33
17 = 38
18 = 39
19 = 40
20 = 41
21 = 46
22 = 47
23 = 48
24 = 49
25 = 54
26 = 55
27 = 56
28 = 57
29 = 62
30 = 63
31 = 64
32 = 65
33 = 70
34 = 71
35 = 72
36 = 73
37 = 78
38 = 79
39 = 80
