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A000415 Numbers that are the sum of 2 but no fewer nonzero squares. 10
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 (list; graph; refs; listen; history; text; internal format)
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. [From Max Alekseyev, Jan 21 2010]

Nonsquare positive integers D such that Pell equation y^2 - D*x^2 = -1 has rational solutions. [From Max Alekseyev, Mar 09 2010]

Nonsquares for which all 4k+3 primes in the integer's canonical form occur with even multiplicity. [From Ant King, Nov 02 2010]

REFERENCES

Guy, Richard. K.; Every Number is Expressible as the Sum of How Many Polygonal Numbers? The American Mathematical Monthly, Vol. 101, No. 2, (February 1994), pp. 169-172. [From Ant King, Nov 02 2010]

Grosswald, E.; Representation of Integers as Sums of Squares, Springer-Verlag, New York Inc., (1985), p.15. [From Ant King, Nov 02 2010]

LINKS

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

Eric Weisstein's World of Mathematics, Square Number

Index entries for sequences related to sums of squares

FORMULA

Equals A000404 - A134422 - 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[ # ]] &] [From Ant King, Nov 02 2010]

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

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Last modified September 21 17:15 EDT 2014. Contains 247025 sequences.