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A166477
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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).
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3
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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
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OFFSET
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2,1
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COMMENTS
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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
-- ------- ------------------------------------------------
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
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
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LINKS
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EXAMPLE
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For n=14, x=20; corresponding value of t is 5 since 14 = 20*21/(5*6).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Deleted an 8 between 14 and 185. - R. J. Mathar, Oct 23 2010
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STATUS
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approved
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