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A084645 Hypotenuses for which there exists a unique integer-sided triangle. 41
5, 10, 13, 15, 17, 20, 26, 29, 30, 34, 35, 37, 39, 40, 41, 45, 51, 52, 53, 55, 58, 60, 61, 68, 70, 73, 74, 78, 80, 82, 87, 89, 90, 91, 95, 97, 101, 102, 104, 105, 106, 109, 110, 111, 113, 115, 116, 117, 119, 120, 122, 123, 135, 136, 137, 140, 143, 146, 148, 149 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers whose square is uniquely decomposable into the sum of two nonzero squares: these are those numbers with exactly one prime divisor of the form 4k+1 with multiplicity one. - Jean-Christophe Hervé, Nov 11 2013
LINKS
Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Zak Seidov)
Eric Weisstein's World of Mathematics, Pythagorean Triple
FORMULA
Terms are obtained by the products A004144(k)*A002144(p) for k, p > 0, ordered by increasing values. - Jean-Christophe Hervé, Nov 12 2013
A046080(a(n)) = 1, A046109(a(n)) = 12. - Jean-Christophe Hervé, Dec 01 2013
MATHEMATICA
r[a_] := {b, c} /. {ToRules[ Reduce[0 < b < c && a^2 == b^2 + c^2, {b, c}, Integers]]}; Select[ Range[150], Length[r[#]] == 1 &] (* Jean-François Alcover, Oct 22 2012 *)
CROSSREFS
Cf. A004144 (0), 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), A290504 (18), A290505 (19), A097103 (22), A097244 (31), A097245 (37), A097282 (40), A097626 (67).
Sequence in context: A360020 A334757 A209922 * A343113 A354235 A313379
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jun 01 2003
STATUS
approved

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Last modified March 28 21:57 EDT 2024. Contains 371254 sequences. (Running on oeis4.)