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A290500
Hypotenuses for which there exist exactly 9 distinct integer triangles.
24
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
OFFSET
1,1
COMMENTS
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.
LINKS
Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Hamdi Sahloul)
FORMULA
Terms are obtained by the product A004144(k)*A002144(p)^9 for k, p > 0 ordered by increasing values.
EXAMPLE
a(1) = 1953125 = 5^9, a(5) = 11718750 = 2*3*5^9, a(101) = 375000000 = 2^6*3*5^9.
MATHEMATICA
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 *)
CROSSREFS
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).
Sequence in context: A220290 A186578 A186579 * A377162 A016821 A016857
KEYWORD
nonn
AUTHOR
Hamdi Sahloul, Aug 04 2017
STATUS
approved