

A290501


Hypotenuses for which there exist exactly 11 distinct integer triangles.


24



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



