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A084645 Hypotenuses for which there exists a unique integer triangle. 34
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 with exactly one prime divisor of the form 4k+1 with multiplicity one. - Jean-Christophe Hervé, Nov 11 2013

LINKS

Zak Seidov, Table of n, a(n) for n = 1..1000

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. A002144, A006339, A046080, A046109, A083025.

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: A071821 A201012 A209922 * A313379 A092604 A313380

Adjacent sequences:  A084642 A084643 A084644 * A084646 A084647 A084648

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jun 01 2003

STATUS

approved

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Last modified May 19 13:18 EDT 2019. Contains 323393 sequences. (Running on oeis4.)