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A290505
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Hypotenuses for which there exist exactly 19 distinct integer triangles.
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24
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203125, 265625, 406250, 453125, 531250, 578125, 609375, 640625, 796875, 812500, 828125, 906250, 953125, 1062500, 1140625, 1156250, 1218750, 1281250, 1359375, 1390625, 1421875, 1515625, 1578125, 1593750, 1625000, 1656250, 1703125, 1734375, 1765625, 1812500
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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 19 different ways into the sum of two nonzero squares: these are those with exactly two distinct prime divisors of the form 4k+1 with one, and six respective multiplicities, or with only one prime divisor of this form with multiplicity nineteen.
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 203125 = 5^6*13, a(5) = 531250 = 2*5^6*17, a(281) = 12796875 = 3^2*5^6*7*13.
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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[12796875], Length[r[#]] == 19 &] (* 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), A290500 (9), A097225 (10), A290501 (11), A097226 (12), A097102 (13), A290502 (14), A290503 (15), A097238 (16), A097239 (17), A290504 (18), 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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