

A000415


Numbers that are the sum of 2 but no fewer nonzero squares.


13



2, 5, 8, 10, 13, 17, 18, 20, 26, 29, 32, 34, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 68, 72, 73, 74, 80, 82, 85, 89, 90, 97, 98, 101, 104, 106, 109, 113, 116, 117, 122, 125, 128, 130, 136, 137, 145, 146, 148, 149, 153, 157, 160, 162, 164, 170, 173, 178, 180, 181
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OFFSET

1,1


COMMENTS

Only these numbers can occur as discriminants of quintic polynomials with solvable Galois group F20.  Artur Jasinski, Oct 25 2007
Complement of A022544 in the nonsquare positive integers A000037.  Max Alekseyev, Jan 21 2010
Nonsquare positive integers D such that Pell equation y^2  D*x^2 = 1 has rational solutions.  Max Alekseyev, Mar 09 2010
Nonsquares for which all 4k+3 primes in the integer's canonical form occur with even multiplicity.  Ant King, Nov 02 2010


REFERENCES

Grosswald, E.; Representation of Integers as Sums of Squares, SpringerVerlag, New York Inc., (1985), p.15.  Ant King, Nov 02 2010


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000
R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169172.  Ant King, Nov 02 2010
Eric Weisstein's World of Mathematics, Square Number
Index entries for sequences related to sums of squares


FORMULA

Equals A000404A134422.  Artur Jasinski, Oct 25 2007


MATHEMATICA

c = {}; Do[Do[k = a^2 + b^2; If[IntegerQ[Sqrt[k]], [null], AppendTo[c, k]], {a, 1, 100}], {b, 1, 100}]; Union[c] (* Artur Jasinski, Oct 25 2007 *)
Select[Range[181], Length[PowersRepresentations[ #, 2, 2]]>0 && !IntegerQ[Sqrt[ # ]] &] (* Ant King, Nov 02 2010 *)


PROG

(PARI) is(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]%2 && f[i, 1]%4==3, return(0))); !issquare(n) \\ Charles R Greathouse IV, Feb 07 2017


CROSSREFS

Cf. A000404, A000419, A001481, A002828, A009003, A134422.
Sequence in context: A000404 A025284 A140328 * A172000 A096691 A202057
Adjacent sequences: A000412 A000413 A000414 * A000416 A000417 A000418


KEYWORD

nonn,nice


AUTHOR

N. J. A. Sloane and J. H. Conway


EXTENSIONS

More terms from Arlin Anderson (starship1(AT)gmail.com)


STATUS

approved



