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

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

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

Georg Fischer, Table of n, a(n) for n = 1..10000

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

Crossrefs

Cf. A004432, A001974.

Sequence in context: A114985 A344703 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