

A009177


Numbers that are the hypotenuses of more than one Pythagorean triangle.


8



25, 50, 65, 75, 85, 100, 125, 130, 145, 150, 169, 170, 175, 185, 195, 200, 205, 221, 225, 250, 255, 260, 265, 275, 289, 290, 300, 305, 325, 338, 340, 350, 365, 370, 375, 377, 390, 400, 410, 425, 435, 442, 445, 450, 455, 475, 481, 485, 493, 500, 505, 507, 510, 520, 525
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OFFSET

1,1


COMMENTS

Also, hypotenuses of Pythagorean triangles in Pythagorean triples (a, b, c, a < b < c) such that a and b are the hypotenuses of Pythagorean triangles, where the Pythagorean triples (x1, y1, a) and (x2, y2, b) are similar triangles. Sequence gives c values.  Naohiro Nomoto
Any multiple of a term of this sequence is also a term. The primitive elements are the products of two primes, not necessarily distinct, that are == 1 (mod 4): A121387.  Franklin T. AdamsWatters, Dec 21 2015
Numbers appearing more than once in A009000.  Sean A. Irvine, Apr 20 2018


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sums of squares


FORMULA

Of the form b(i)*b(j)*k, where b(n) is A004431(n). Numbers whose prime factorization includes at least 2 (not necessarily distinct) primes congruent to 1 mod 4.  Franklin T. AdamsWatters, May 03 2006. [Typo corrected by Ant King, Jul 17 2008]


EXAMPLE

25^2 = 24^2 + 7^2 = 20^2 + 15^2.
E.g., (a = 15, b = 20, c = 25, a^2 + b^2=c^2); 15 and 20 are the hypotenuses of Pythagorean triangles. The Pythagorean triples (9, 12, 15) and (12, 16, 20) are similar triangles. So c = 25 is in the sequence.  Naohiro Nomoto


MAPLE

filter:= proc(n) add(`if` (t[1] mod 4 = 1, t[2], 0), t = ifactors(n)[2]) >= 2 end proc:
select(filter, [$1..1000]); # Robert Israel, Dec 21 2015


MATHEMATICA

Clear[lst, f, n, i, k]; f[n_] := Module[{i = 0, k = 0}, Do[If[Sqrt[n^2  i^2] == IntegerPart[Sqrt[n^2  i^2]], k++], {i, n  1, 1, 1}]; k]; lst = {}; Do[If[f[n] > 2, AppendTo[lst, n]], {n, 4*5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 12 2009 *)


CROSSREFS

Cf. A004431, A009000, A118882, A121387.
Sequence in context: A236849 A236834 A033902 * A118882 A085625 A116490
Adjacent sequences: A009174 A009175 A009176 * A009178 A009179 A009180


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



