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URL: https://oeis.org/A001422

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A001422
Numbers which are not the sum of distinct squares.
32
2, 3, 6, 7, 8, 11, 12, 15, 18, 19, 22, 23, 24, 27, 28, 31, 32, 33, 43, 44, 47, 48, 60, 67, 72, 76, 92, 96, 108, 112, 128
OFFSET
1,1
COMMENTS
This is the complete list (Sprague).
REFERENCES
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.
Harry L. Nelson, The Partition Problem, J. Rec. Math., 20 (1988), 315-316.
J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 222.
LINKS
R. E. Dressler and T. Parker, 12,758, Math. Comp. 28 (1974), 313-314.
R. Sprague, Über Zerlegungen in ungleiche Quadratzahlen, Math. Z. 51, (1948), 289-290.
Eric Weisstein's World of Mathematics, Square Number.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Complement of A003995. Subsequence of A004441.
Cf. A025524 (number of numbers not the sum of distinct n-th-order polygonal numbers)
Cf. A007419 (largest number not the sum of distinct n-th-order polygonal numbers)
Cf. A053614, A121405 (corresponding sequences for triangular and pentagonal numbers)
Cf. A001476, A046039, A194768, A194769 for 3rd, 4th, 5th, 6th powers.
Cf. A001661.
Sequence in context: A064472 A276887 A276517 * A097757 A304028 A155152
KEYWORD
nonn,fini,full
AUTHOR
N. J. A. Sloane, Jeff Adams (jeff.adams(AT)byu.net)
STATUS
approved