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A290504 Hypotenuses for which there exist exactly 18 distinct integer triangles. 24
3814697265625, 7629394531250, 11444091796875, 15258789062500, 22888183593750, 26702880859375, 30517578125000, 34332275390625, 41961669921875, 45776367187500, 53405761718750, 61035156250000, 68664550781250, 72479248046875, 80108642578125, 83923339843750 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers whose square is decomposable in 18 different ways into the sum of two nonzero squares: these are those with only one prime divisor of the form 4k+1 with multiplicity eighteen.
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)^18 for k, p > 0 ordered by increasing values.
EXAMPLE
a(1) = 3814697265625 = 5^18, a(5) = 22888183593750 = 2*3*5^18, a(101) = 732421875000000 = 2^6*3*5^18.
MATHEMATICA
r[a_]:={b, c}/.{ToRules[Reduce[0<b<c && a^2 == b^2 + c^2, {b, c}, Integers]]}; Select[Range[732421875000000], Length[r[#]] == 18 &] (* 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), A290503 (15), A097238 (16), A097239 (17), A290505 (19), A097103 (22), A097244 (31), A097245 (37), A097282 (40), A097626 (67).
Sequence in context: A230485 A172646 A222558 * A172630 A186912 A288284
KEYWORD
nonn
AUTHOR
Hamdi Sahloul, Aug 04 2017
STATUS
approved

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Last modified May 24 22:09 EDT 2024. Contains 372782 sequences. (Running on oeis4.)