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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 (list; graph; refs; listen; history; text; internal format)
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(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

MATHEMATICA

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 *)

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

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Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)