Search: id:A004215
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%I A004215 M4349
%S A004215 7,15,23,28,31,39,47,55,60,63,71,79,87,92,95,103,111,112,119,124,127,
%T A004215 135,143,151,156,159,167,175,183,188,191,199,207,215,220,223,231,239,
%U A004215 240,247,252,255,263,271,279,284,287,295,303,311,316,319,327,335,343
%N A004215 Numbers that are the sum of 4 but no fewer nonzero squares.
%C A004215 If n is in the sequence and k is an odd positive integer then n^k is 
               in the sequence because n^k is of the form 4^i(8j+7). - Farideh Firoozbakht 
               (mymontain(AT)yahoo.com), Nov 23 2006
%C A004215 Numbers whose cubes do not have a partition as a sum of 3 squares. a(n)^3=A134738(n) 
               - Artur Jasinski (grafix(AT)csl.pl), Nov 07 2007
%D A004215 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A004215 L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 
               256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see 
               vol. 2, p. 261.
%D A004215 L. J. Mordell, A new Waring's problem with squares of linear forms, Quart. 
               J. Math., 1 (1930), 276-288 (see p. 283).
%D A004215 E. Poznanski, 1901. Pierwiastki pierwotne liczb pierwszych. Warszawa, 
               pp. 1-63.
%D A004215 W. Sierpinski, 1925. Teorja Liczb. pp. 1-410 (p. 125).
%D A004215 S. Uchiyama, A five-square theorem, Publ. Res. Math. Sci., Vol 13, Number 
               1 (1977), 301-305.
%D A004215 David Wells, The Penguin Dictionary of Curious and Interesting Numbers, 
               entry 4181.
%H A004215 T. D. Noe, <a href="b004215.txt">Table of n, a(n) for n=1..10000</a>
%H A004215 R. T. Bumby, <a href="http://www.math.rutgers.edu/~bumby/squares1.pdf">
               Sums Of Four Squares</a>
%H A004215 Steve Waterman, <a href="http://watermanpolyhedron.com/MISSING.html">
               Missing numbers formula</a>
%H A004215 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SquareNumber.html">Square Number</a>
%H A004215 <a href="Sindx_Su.html#ssq">Index entries for sequences related to sums 
               of squares</a>
%F A004215 a(n) = A044075(n)/2. Ray Chandler, Jan 30 2009
%F A004215 Numbers of the form 4^i(8j+7), i >= 0, j >= 0.
%F A004215 Products of the form A000302(i)*A004771(j), i,j>=0. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 29 2006
%t A004215 Sort[Flatten[Table[4^i(8j + 7), {i, 0, 2}, {j, 0, 42}]]] (Alonso Delarte 
               (alonso.delarte(AT)gmail.com), Jul 05 2005)
%t A004215 b = Table[x^3, {x, 1, 300}]; a = {}; Do[Do[Do[AppendTo[a, (x^2 + y^2 
               + z^2)^3], {x, 0, 30}], {y, 0, 30}], {z, 0, 30}]; Union[a]; k = Complement[b, 
               a]; k^(1/3) - Artur Jasinski (grafix(AT)csl.pl), Nov 07 2007
%o A004215 (PARI) isA004215(n)={ local(fouri,j) ; fouri=1 ; while( n >=7*fouri, 
               if( n % fouri ==0, j= n/fouri -7 ; if( j % 8 ==0, return(1) ) ; ) 
               ; fouri *= 4 ; ) ; return(0) ; } { for(n=1,400, if(isA004215(n), 
               print1(n,",") ; ) ; ) ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 22 2006
%Y A004215 Cf. A000378, A002828, A055039, A072401, A125084, A134738, A134739.
%Y A004215 Sequence in context: A128840 A041935 A041092 this_sequence A043449 A136768 
               A031490
%Y A004215 Adjacent sequences: A004212 A004213 A004214 this_sequence A004216 A004217 
               A004218
%K A004215 nonn,nice
%O A004215 1,1
%A A004215 N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)
%E A004215 More terms from Arlin Anderson (starship1(AT)gmail.com). Additional comments 
               from Jud McCranie (j.mccranie(AT)comcast.net), Mar 19 2000.

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