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 A024803 Numbers that are the sum of 3 distinct nonzero squares, including repetitions. 5

%I

%S 14,21,26,29,30,35,38,41,42,45,46,49,50,53,54,56,59,61,62,62,65,66,69,

%T 69,70,74,74,75,77,77,78,81,83,84,86,86,89,89,90,90,91,93,94,94,98,98,

%U 101,101,101,104,105,105,106,107,109,110,110,110,113,114,115,116,117

%N Numbers that are the sum of 3 distinct nonzero squares, including repetitions.

%C Numbers n = x^2 + y^2 + z^2, with 0<x<y<z; repeat n for each such representation.

%C Records of 1,2,3 etc. repetitions are set by the numbers 14, 62, 101, 161, 206, 314, 341, 446, 689, 734, 854, 1106, 1154, 1286, 1454 etc.; see A025415. - _R. J. Mathar_, Mar 15 2007

%H Vincenzo Librandi, <a href="/A024803/b024803.txt">Table of n, a(n) for n = 1..9000</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%e 14 = 1^2 + 2^2 + 3^2.

%e 62 = 1^2 + 5^2 + 6^2 = 2^2 + 3^2 + 7^2.

%e 105 = 1^2 + 2^2 + 10^2 = 4^2 + 5^2 + 8^2.

%e 122 = 3^2 + 7^2 + 8^2 = 4^2 + 5^2 + 9^2.

%p A024803 := proc(n) local a,x,y,z ; a := 0 ; for x from 1 to floor(sqrt(n)) do for y from x+1 to floor(sqrt(n-x^2)) do z := n-x^2-y^2 ; if issqr(z) then z := sqrt(z) ; if z>y and z>x then a := a+1 ; fi ; fi ; od ; od ; RETURN(a) ; end: for n from 1 to 200 do a := A024803(n) : for i from 1 to a do printf("%d ",n) ; od ; od : # _R. J. Mathar_, Mar 15 2007

%t a=1;b=2;c=3;lst={};Do[Do[Do[s=a^2+b^2+c^2;AppendTo[lst,s],{a,1,b-1}],{b,a,c-1}],{c,b,25}];lst;Take[Sort[lst],123] (* _Vladimir Joseph Stephan Orlovsky_, Jan 22 2009 *)

%t Sort[Total/@Subsets[Range^2,{3}]] (* _Harvey P. Dale_, Mar 22 2012 *)

%Y Cf. A004432, A001974.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_

%E Zak Seidov pointed out that there were errors. These have now been corrected. - _N. J. A. Sloane_, Dec 05 2006

%E More terms from _R. J. Mathar_, Mar 15 2007

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)