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A010814 Perimeters of integer-sided right triangles.

%I A010814 #43 Mar 22 2025 18:44:10
%S A010814 12,24,30,36,40,48,56,60,70,72,80,84,90,96,108,112,120,126,132,140,
%T A010814 144,150,154,156,160,168,176,180,182,192,198,200,204,208,210,216,220,
%U A010814 224,228,234,240,252,260,264,270,276,280,286,288,300,306,308,312,320,324
%N A010814 Perimeters of integer-sided right triangles.
%C A010814 A number k is in this sequence iff k is a multiple of some term in A024364.
%H A010814 Ray Chandler, <a href="/A010814/b010814.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Vincenzo Librandi)
%H A010814 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html">Pythagorean Triples and Online Calculators</a>.
%H A010814 <a href="/index/Ps#PyTrip">Index entries related to Pythagorean Triples</a>.
%p A010814 isA010814 := proc(an) local a::integer,b::integer,c::integer ; for c from 1 to floor(an/2) do for a from floor(c/sqrt(2)) to c-1 do if issqr(c^2-a^2) then b := sqrt(c^2-a^2) ; if a+b+c = an then RETURN(true) ; fi ; fi ; od ; od : RETURN(false) ; end : for n from 3 to 400 do if isA010814(n) then printf("%d,",n) ; fi ; od ; # _R. J. Mathar_, Jun 08 2006
%t A010814 lst={};Do[Do[If[IntegerQ[c=Sqrt[a^2+b^2]],AppendTo[lst,a+b+c]],{b,a-1,Floor[Sqrt[a]],-1}],{a,4,4*5!}];Take[Union@lst,100] (* _Vladimir Joseph Stephan Orlovsky_, Nov 23 2010 *)
%t A010814 q[n_] := EvenQ[n] && Module[{d = Divisors[n/2]}, AnyTrue[Range[3, Length[d]], d[[#]] < 2 * d[[#-1]] &]]; Select[Range[350], q] (* _Amiram Eldar_, Oct 19 2024 *)
%o A010814 (PARI) select( {is_A010814(n)=n%2==0&&is_A005279(n\2)}, [1..333]) \\ _M. F. Hasler_, Mar 20 2025
%Y A010814 Twice A005279.
%Y A010814 Cf. A024364.
%K A010814 nonn,easy
%O A010814 1,1
%A A010814 Ben Manvel (manvel(AT)lagrange.math.colostate.edu)
%E A010814 More terms from _Ray Chandler_, Mar 13 2004