1,1

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

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

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

L. J. Mordell, A new Waring's problem with squares of linear forms, Quart. J. Math., 1 (1930), 276-288 (see p. 283).

E. Poznanski, 1901. Pierwiastki pierwotne liczb pierwszych. Warszawa, pp. 1-63.

W. Sierpinski, 1925. Teorja Liczb. pp. 1-410 (p. 125).

S. Uchiyama, A five-square theorem, Publ. Res. Math. Sci., Vol 13, Number 1 (1977), 301-305.

David Wells, The Penguin Dictionary of Curious and Interesting Numbers, entry 4181.

T. D. Noe, Table of n, a(n) for n=1..10000

R. T. Bumby, Sums Of Four Squares

Steve Waterman, Missing numbers formula

Eric Weisstein's World of Mathematics, Square Number

Index entries for sequences related to sums of squares

a(n) = A044075(n)/2. Ray Chandler, Jan 30 2009

Numbers of the form 4^i(8j+7), i >= 0, j >= 0.

Products of the form A000302(i)*A004771(j), i,j>=0. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 29 2006

Sort[Flatten[Table[4^i(8j + 7), {i, 0, 2}, {j, 0, 42}]]] (Alonso Delarte (alonso.delarte(AT)gmail.com), Jul 05 2005)

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

(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

Cf. A000378, A002828, A055039, A072401, A125084, A134738, A134739.

Sequence in context: A128840 A041935 A041092 this_sequence A043449 A136768 A031490

Adjacent sequences: A004212 A004213 A004214 this_sequence A004216 A004217 A004218

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)

More terms from Arlin Anderson (starship1(AT)gmail.com). Additional comments from Jud McCranie (j.mccranie(AT)comcast.net), Mar 19 2000.