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Search: id:A097101
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| A097101 |
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Numbers n that are the hypotenuse of exactly 7 distinct integer-sided right triangles, i.e. n^2 can be written as a sum of two squares in 7 ways. |
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6
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| 325, 425, 650, 725, 845, 850, 925, 975, 1025, 1275, 1300, 1325, 1445, 1450, 1525, 1690, 1700, 1825, 1850, 1950, 2050, 2175, 2225, 2275, 2425, 2525, 2535, 2550, 2600, 2650, 2725, 2775, 2825, 2873, 2890, 2900, 2925, 2975
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Comment from R. J. Mathar, Feb 26 2008, edited by Zak Seidov May 12 2008: (Start) There are nonsquare x which can be written as a sum of 2 nonzero squares in exactly 7 different ways and which are by definition not in this sequence.
203125 = (125*sqrt(13))^2 is the first example: 203125 = 625 + 202500 = 10404 + 192721 = 18225 + 184900= 22500 + 180625= 62500 + 140625= 69169 + 133956= 84100 + 119025.
The second and third examples are 265625 = (125*sqrt(17))^2 and 406250=(125*sqrt(26))^2. (End)
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FORMULA
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Equals {n: A025426(n^2)=7}.
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EXAMPLE
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Example supplied by R. J. Mathar, Feb 26 2008: the smallest number that can be written as a sum of two nonzero squares in 7 different ways is 105625 = 325^2:
1296 + 104329 = 105625 = 325^2
6400 + 99225 = 105625 = 325^2
8281 + 97344 = 105625 = 325^2
15625 + 90000 = 105625 = 325^2
27225 + 78400 = 105625 = 325^2
38025 + 67600 = 105625 = 325^2
41616 + 64009 = 105625 = 325^2.
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CROSSREFS
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Cf. A084645, A084646, A084647, A084648, A084649, A097102, A097103.
Sequence in context: A159976 A159844 A000443 this_sequence A025294 A025313 A025286
Adjacent sequences: A097098 A097099 A097100 this_sequence A097102 A097103 A097104
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KEYWORD
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nonn
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AUTHOR
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Jim Buddenhagen (jbuddenh(AT)gmail.com), Sep 15 2004
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EXTENSIONS
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Definition and comments corrected by Zak Seidov, Feb 26 2008, May 12 2008
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