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%I #41 May 14 2020 11:14:37
%S 2,3,6,7,8,11,12,15,18,19,22,23,24,27,28,31,32,33,43,44,47,48,60,67,
%T 72,76,92,96,108,112,128
%N Numbers which are not the sum of distinct squares.
%C This is the complete list (Sprague).
%D S. Lin, Computer experiments on sequences which form integral bases, pp. 365-370 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.
%D Harry L. Nelson, The Partition Problem, J. Rec. Math., 20 (1988), 315-316.
%D J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 222.
%H R. E. Dressler and T. Parker, <a href="http://dx.doi.org/10.1090/S0025-5718-1974-0327652-1">12,758</a>, Math. Comp. 28 (1974), 313-314.
%H T. Sillke, <a href="http://www.mathematik.uni-bielefeld.de/~sillke/SEQUENCES/series010">Not the sum of distinct squares</a>
%H R. Sprague, <a href="https://dx.doi.org/10.1007/BF01181594">Über Zerlegungen in ungleiche Quadratzahlen</a>, Math. Z. 51, (1948), 289-290.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquareNumber.html">Square Number.</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F Complement of A003995.
%t nn=50; t=Rest[CoefficientList[Series[Product[(1+x^(k*k)), {k,nn}], {x,0,nn*nn}], x]]; Flatten[Position[t,0]] (* _T. D. Noe_, Jul 24 2006 *)
%o (PARI) select( is_A001422(n,m=n)={m^2>n&& m=sqrtint(n); n!=m^2&&!while(m>1,isSumOfSquares(n-m^2,m--)&&return)}, [1..128]) \\ _M. F. Hasler_, Apr 21 2020
%Y Cf. A025524 (number of numbers not the sum of distinct n-th-order polygonal numbers)
%Y Cf. A007419 (largest number not the sum of distinct n-th-order polygonal numbers)
%Y Cf. A053614, A121405 (corresponding sequences for triangular and pentagonal numbers)
%Y Cf. A033461, A276517.
%Y Cf. A001476, A046039, A194768, A194769 for 3rd, 4th, 5th, 6th powers.
%K nonn,fini,full
%O 1,1
%A _N. J. A. Sloane_, Jeff Adams (jeff.adams(AT)byu.net)
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