A290501 Hypotenuses for which there exist exactly 11 distinct integer triangles.

48828125, 97656250, 146484375, 195312500, 292968750, 341796875, 390625000, 439453125, 537109375, 585937500, 683593750, 781250000, 878906250, 927734375, 1025390625, 1074218750, 1123046875, 1171875000, 1318359375, 1367187500, 1513671875, 1562500000, 1611328125

Offset

1,1

Comments

Numbers whose square is decomposable in 11 different ways into the sum of two nonzero squares: these are those with only one prime divisor of the form 4k+1 with multiplicity eleven.

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)^11 for k, p > 0 ordered by increasing values.

Example

a(1) = 48828125 = 5^11, a(5) = 292968750 = 2*3*5^11, a(101) = 9375000000 = 2^6*3*5^11.

Mathematica

r[a_]:={b, c}/.{ToRules[Reduce[0<b<c && a^2 == b^2 + c^2, {b, c}, Integers]]}; Select[Range[9375000000], Length[r[#]] == 11 &] (* Vincenzo Librandi, Mar 01 2016 *)

Crossrefs

Cf. A002144, A006339, A046080, A046109, A083025.

Cf. A004144 (0), A084645 (1), A084646 (2), A084647 (3), A084648 (4), A084649 (5), A097219 (6), A097101 (7), A290499 (8), A290500 (9), A097225 (10), 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: A300568 A210334 A022259 * A016823 A016859 A016979

Adjacent sequences: A290498 A290499 A290500 * A290502 A290503 A290504

Keyword

nonn

Author

Hamdi Sahloul, Aug 04 2017

Status

approved