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A290500
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Hypotenuses for which there exist exactly 9 distinct integer triangles.
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24
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1953125, 3906250, 5859375, 7812500, 11718750, 13671875, 15625000, 17578125, 21484375, 23437500, 27343750, 31250000, 35156250, 37109375, 41015625, 42968750, 44921875, 46875000, 52734375, 54687500, 60546875, 62500000, 64453125, 70312500, 74218750, 82031250
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OFFSET
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1,1
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COMMENTS
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Numbers whose square is decomposable in 9 different ways into the sum of two nonzero squares: these are those with only one prime divisor of the form 4k+1 with multiplicity nine.
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LINKS
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FORMULA
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Terms are obtained by the product A004144(k)*A002144(p)^9 for k, p > 0 ordered by increasing values.
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EXAMPLE
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a(1) = 1953125 = 5^9, a(5) = 11718750 = 2*3*5^9, a(101) = 375000000 = 2^6*3*5^9.
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MATHEMATICA
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r[a_]:={b, c}/.{ToRules[Reduce[0<b<c && a^2 == b^2 + c^2, {b, c}, Integers]]}; Select[Range[375000000], Length[r[#]] == 9 &] (* Vincenzo Librandi, Mar 01 2016 *)
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CROSSREFS
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Cf. A004144 (0), A084645 (1), A084646 (2), A084647 (3), A084648 (4), A084649 (5), A097219 (6), A097101 (7), A290499 (8), A097225 (10), A290501 (11), A097226 (12), A097102 (13), A290502 (14), A290503 (15), A097238 (16), A097239 (17), A290504 (18), A290505 (19), A097103 (22), A097244 (31), A097245 (37), A097282 (40), A097626 (67).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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