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URL: https://oeis.org/A290503

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A290503
Hypotenuses for which there exist exactly 15 distinct integer triangles.
24
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. 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: A172852 A172694 A384643 * A172889 A017087 A017171
KEYWORD
nonn
AUTHOR
Hamdi Sahloul, Aug 04 2017
STATUS
approved