A004214 Positive numbers that are not the sum of three nonzero squares.

1, 2, 4, 5, 7, 8, 10, 13, 15, 16, 20, 23, 25, 28, 31, 32, 37, 39, 40, 47, 52, 55, 58, 60, 63, 64, 71, 79, 80, 85, 87, 92, 95, 100, 103, 111, 112, 119, 124, 127, 128, 130, 135, 143, 148, 151, 156, 159, 160, 167, 175, 183, 188, 191, 199, 207, 208, 215, 220, 223, 231

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Not of the form x^2 + y^2 + z^2 with x, y, z >= 1.

Complement of A000408, but skipping the zero. - R. J. Mathar, Nov 23 2006

A025427(a(n)) = 0. - Reinhard Zumkeller, Feb 26 2015

Examples

			The smallest numbers that are the sums of 3 nonzero squares are 3=1+1+1, 6=1+1+4, 9=1+4+4, etc.
		

References

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

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000
• David S. Bettes, Letter to N. J. A. Sloane, Nov 05 1976.
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000408, A025427.

Programs

Haskell

a004214 n = a004214_list !! (n-1)
a004214_list = filter ((== 0) . a025427) [1..]
-- Reinhard Zumkeller, Feb 26 2015

Maple

gf := sum(sum(sum(q^(x^2+y^2+z^2), x=1..25), y=1..25), z=1..25): s := series(gf, q, 500): for n from 1 to 500 do if coeff(s, q, n)=0 then printf(`%d,`,n) fi:od:

Mathematica

f[n_] := Flatten[Position[Take[Rest[CoefficientList[Sum[x^(i^2), {i, n}]^3, x]], n^2], 0]];f[16] (* Ray Chandler, Dec 06 2006 *)

PARI

isA000408(n)={ local(a,b) ; a=1; while(a^2+1A004214(n)={ return(! isA000408(n)) ; }
n=1 ; for(an=1,20000, if(isA004214(an), print(n," ",an); n++)) \\ R. J. Mathar, Nov 23 2006

Extensions

More terms from James Sellers, Apr 20 2001

Name clarified by Wolfdieter Lang, Apr 04 2013