

A024803


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


5



14, 21, 26, 29, 30, 35, 38, 41, 42, 45, 46, 49, 50, 53, 54, 56, 59, 61, 62, 62, 65, 66, 69, 69, 70, 74, 74, 75, 77, 77, 78, 81, 83, 84, 86, 86, 89, 89, 90, 90, 91, 93, 94, 94, 98, 98, 101, 101, 101, 104, 105, 105, 106, 107, 109, 110, 110, 110, 113, 114, 115, 116, 117
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OFFSET

1,1


COMMENTS

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


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..9000
Index entries for sequences related to sums of squares


EXAMPLE

14 = 1^2 + 2^2 + 3^2.
62 = 1^2 + 5^2 + 6^2 = 2^2 + 3^2 + 7^2.
105 = 1^2 + 2^2 + 10^2 = 4^2 + 5^2 + 8^2.
122 = 3^2 + 7^2 + 8^2 = 4^2 + 5^2 + 9^2.


MAPLE

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(nx^2)) do z := nx^2y^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


MATHEMATICA

a=1; b=2; c=3; lst={}; Do[Do[Do[s=a^2+b^2+c^2; AppendTo[lst, s], {a, 1, b1}], {b, a, c1}], {c, b, 25}]; lst; Take[Sort[lst], 123] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2009 *)
Sort[Total/@Subsets[Range[10]^2, {3}]] (* Harvey P. Dale, Mar 22 2012 *)


CROSSREFS

Cf. A004432, A001974.
Sequence in context: A093994 A114985 A001944 * A004432 A025339 A224771
Adjacent sequences: A024800 A024801 A024802 * A024804 A024805 A024806


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling


EXTENSIONS

Zak Seidov pointed out that there were errors. These have now been corrected.  N. J. A. Sloane, Dec 05 2006
More terms from R. J. Mathar, Mar 15 2007


STATUS

approved



