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 A000415 Numbers that are the sum of 2 but no fewer nonzero squares. 17
 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. - 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 E. Grosswald, Representation of Integers as Sums of Squares, Springer-Verlag, 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), 169-172. - Ant King, Nov 02 2010 Eric Weisstein's World of Mathematics, Square Number Index entries for sequences related to sums of squares FORMULA { A000404 } minus { 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[ # ]] &] (* 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 (Python) from itertools import count, islice from sympy import factorint def A000415_gen(startvalue=2): # generator of terms >= startvalue for n in count(max(startvalue, 2)): f = factorint(n).items() if any(e&1 for p, e in f if p&3<3) and not any(e&1 for p, e in f if p&3==3): yield n A000415_list = list(islice(A000415_gen(), 20)) # Chai Wah Wu, Aug 01 2023 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 July 23 17:14 EDT 2024. Contains 374552 sequences. (Running on oeis4.)