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A290499
Hypotenuses for which there exist exactly 8 distinct integer triangles.
24
390625, 781250, 1171875, 1562500, 2343750, 2734375, 3125000, 3515625, 4296875, 4687500, 5468750, 6250000, 7031250, 7421875, 8203125, 8593750, 8984375, 9375000, 10546875, 10937500, 12109375, 12500000, 12890625, 14062500, 14843750, 16406250, 16796875, 17187500
OFFSET
1,1
COMMENTS
Numbers whose square is decomposable in 8 different ways into the sum of two nonzero squares: these are those with only one prime divisor of the form 4k+1 with multiplicity eight.
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)^8 for k, p > 0 ordered by increasing values.
EXAMPLE
a(1) = 390625 = 5^8, a(5) = 2343750 = 2*3*5^8, a(101) = 75000000 = 2^6*3*5^8.
MATHEMATICA
r[a_]:={b, c}/.{ToRules[Reduce[0<b<c && a^2 == b^2 + c^2, {b, c}, Integers]]}; Select[Range[75000000], Length[r[#]] == 8 &] (* Vincenzo Librandi, Mar 01 2016 *)
CROSSREFS
Cf. A004144 (0), A084645 (1), A084646 (2), A084647 (3), A084648 (4), A084649 (5), A097219 (6), A097101 (7), A290500 (9), 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: A106778 A164987 A176765 * A375733 A016820 A016856
KEYWORD
nonn
AUTHOR
Hamdi Sahloul, Aug 04 2017
STATUS
approved