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

Author

Hamdi Sahloul, Aug 04 2017

Keywords

• nonn

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.

Examples

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

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Hamdi Sahloul)

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).

Programs

Mathematica

r[a_]:={b, c}/.{ToRules[Reduce[0Vincenzo Librandi, Mar 01 2016 *)

Formula

Terms are obtained by the product A004144(k)*A002144(p)^14 for k, p > 0 ordered by increasing values.