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A166477
Minimum positive integer solution x of equation n=x*(x+1)/(t*(t+1)); that is, ratio of product of two consecutive integers divided by product of two consecutive integers. Here n is a nonsquare integer (see A000037).
3
3, 2, 5, 3, 6, 15, 4, 11, 8, 12, 20, 5, 51, 27, 19, 15, 6, 11, 45, 95, 12, 54, 7, 29, 24, 30, 1343, 54, 84, 14, 185, 95, 65, 15, 41, 35, 42, 560, 9, 23, 140, 287, 24, 17, 39, 105, 1539, 10, 48, 18, 87, 1770, 104, 183, 216, 27, 455, 11, 200, 119, 45, 20, 71, 63, 72, 14060, 99
OFFSET
2,1
COMMENTS
From R. J. Mathar, Oct 23 2010: (Start)
Writing x = (-1 + sqrt(1 + 4*n*t*(t+1))/2, each solution is associated with a Diophantine equation 1 + 4*n*t*(t+1) = s^2. The sequence entries are the leading column if all solutions are presented in rows for a given n:
n Seq # solutions
-- ------- ------------------------------------------------
2 A001652 3, 20, 119, 696, 4059
3 A001571 2, 9, 35, 132, 494, 1845, 6887
4 ...
5 A077262 5, 14, 99, 260, 1785, 4674
6 A077291 3, 8, 35, 84, 351, 836, 3479, 8280
7 A077401 6, 14, 104, 231, 1665, 3689
8 A336625 15, 32, 527, 1104, 17919
9 ...
10 A341895 4, 20, 39, 175, 779, 1500, 6664, 29600
11 11, 21, 230, 429, 4598, 8568
12 8, 15, 119, 216, 1664, 3015, 23183
13 12, 77, 845, 1494, 16302
14 20, 35, 615, 1064, 18444, 31899
15 5, 9, 44, 75, 350, 594, 2759, 4680, 21725, 36849
16 ...
17 51, 84, 3399, 5576
18 27, 44, 935, 1512, 31779
19 19, 285, 455, 6649
20 15, 24, 279, 440, 5015, 7904
(End) [table reformatted by Jon E. Schoenfield, Apr 01 2018]
EXAMPLE
For n=14, x=20; corresponding value of t is 5 since 14 = 20*21/(5*6).
CROSSREFS
Cf. A000037.
Cf. A166478 (associated t). - R. J. Mathar, Oct 23 2010
Sequence in context: A057953 A372679 A129231 * A124332 A364900 A295311
KEYWORD
nonn
AUTHOR
Carmine Suriano, Oct 14 2009
EXTENSIONS
Deleted an 8 between 14 and 185. - R. J. Mathar, Oct 23 2010
STATUS
approved