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

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).

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

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

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, Link to a section of The World of Mathematics.

Index entries for sequences related to sums of squares

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.

2*a9N0 gives A044075.

Cf. A134738, A134739.

Adjacent sequences: A004212 A004213 A004214 this_sequence A004216 A004217 A004218

Sequence in context: A128840 A041935 A041092 this_sequence A043449 A136768 A031490

nonn,nice

njas 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.