A290502 Hypotenuses for which there exist exactly 14 distinct integer triangles.

6103515625, 12207031250, 18310546875, 24414062500, 36621093750, 42724609375, 48828125000, 54931640625, 67138671875, 73242187500, 85449218750, 97656250000, 109863281250, 115966796875, 128173828125, 134277343750, 140380859375, 146484375000, 164794921875

Offset

1,1

Comments

Numbers whose square is decomposable in 14 different ways into the sum of two nonzero squares: these are those with only one prime divisor of the form 4k+1 with multiplicity fourteen.

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)^14 for k, p > 0 ordered by increasing values.

Example

a(1) = 6103515625 = 5^14, a(5) = 36621093750 = 2*3*5^14, a(101) = 1171875000000 = 2^6*3*5^14.

Mathematica

r[a_]:={b, c}/.{ToRules[Reduce[0<b<c && a^2 == b^2 + c^2, {b, c}, Integers]]}; Select[Range[1171875000000], Length[r[#]] == 14 &] (* 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), A290501 (11), A097226 (12), A097102 (13), A290503 (15), A097238 (16), A097239 (17), A290504 (18), A290505 (19), A097103 (22), A097244 (31), A097245 (37), A097282 (40), A097626 (67).

Sequence in context: A234378 A046894 A145552 * A172663 A210727 A004675

Adjacent sequences: A290499 A290500 A290501 * A290503 A290504 A290505

Keyword

nonn

Author

Hamdi Sahloul, Aug 04 2017

Status

approved