A290503 Hypotenuses for which there exist exactly 15 distinct integer triangles.

30517578125, 61035156250, 91552734375, 122070312500, 183105468750, 213623046875, 244140625000, 274658203125, 335693359375, 366210937500, 427246093750, 488281250000, 549316406250, 579833984375, 640869140625, 671386718750, 701904296875, 732421875000

Offset

1,1

Comments

Numbers whose square is decomposable in 15 different ways into the sum of two nonzero squares: these are those with only one prime divisor of the form 4k+1 with multiplicity fifteen.

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)^15 for k, p > 0 ordered by increasing values.

Example

a(1) = 30517578125 = 5^15, a(5) = 183105468750 = 2*3*5^15, a(101) = 5859375000000 = 2^6*3*5^15.

Mathematica

r[a_]:={b, c}/.{ToRules[Reduce[0<b<c && a^2 == b^2 + c^2, {b, c}, Integers]]}; Select[Range[5859375000000], Length[r[#]] == 15 &] (* 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), A290502 (14), A097238 (16), A097239 (17), A290504 (18), A290505 (19), A097103 (22), A097244 (31), A097245 (37), A097282 (40), A097626 (67).

Sequence in context: A364727 A172852 A172694 * A172889 A017087 A017171

Adjacent sequences: A290500 A290501 A290502 * A290504 A290505 A290506

Keyword

nonn

Author

Hamdi Sahloul, Aug 04 2017

Status

approved