login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001974 Numbers that are the sum of 3 distinct squares, i.e., of the form x^2 + y^2 + z^2 with 0 <= x < y < z. 7

%I

%S 5,10,13,14,17,20,21,25,26,29,30,34,35,37,38,40,41,42,45,46,49,50,52,

%T 53,54,56,58,59,61,62,65,66,68,69,70,73,74,75,77,78,80,81,82,83,84,85,

%U 86,89,90,91,93,94,97,98,100,101,104,105,106,107,109,110,113

%N Numbers that are the sum of 3 distinct squares, i.e., of the form x^2 + y^2 + z^2 with 0 <= x < y < z.

%C Also: Numbers which are the sum of two or three distinct nonzero squares. - _M. F. Hasler_, Feb 03 2013

%C According to Halter-Koch (below), a number n is a sum of 3 squares, but not a sum of 3 distinct squares (i.e., is in A001974 but not A000408), if and only if it is of the form 4^j*s, where j >= 0 and s in {1, 2, 3, 6, 9, 11, 18, 19, 22, 27, 33, 43, 51, 57, 67, 99, 102, 123, 163, 177, 187, 267, 627, ?}, where ? denotes at most one unknown number that, if it exists, is > 5*10^10. - _Jeffrey Shallit_, Jan 15 2017

%D Franz Halter-Koch, Darstellung natürlicher Zahlen als Summe von Quadraten, Acta Arithmetica 42 (1982), 11-20.

%H T. D. Noe, <a href="/A001974/b001974.txt">Table of n, a(n) for n=1..1000</a>

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

%e 5 = 0^2 + 1^2 + 2^2.

%t r[n_] := Reduce[0 <= x < y < z && x^2 + y^2 + z^2 == n, {x, y, z}, Integers]; ok[n_] := r[n] =!= False; Select[ Range[113], ok] (* _Jean-François Alcover_, Dec 05 2011 *)

%Y Cf. A001983, A024803, A025339, A025442, A004432.

%Y Cf. A004436 (complement).

%K nonn,easy,nice

%O 1,1

%A _N. J. A. Sloane_

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 16 06:18 EST 2019. Contains 330016 sequences. (Running on oeis4.)