A001422 Numbers which are not the sum of distinct squares.

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

Table of n, a(n) for n=1..31.

R. E. Dressler and T. Parker, 12,758, Math. Comp. 28 (1974), 313-314.

T. Sillke, Not the sum of distinct squares

R. Sprague, Über Zerlegungen in ungleiche Quadratzahlen, Math. Z. 51, (1948), 289-290.

Eric Weisstein's World of Mathematics, Square Number.

Index entries for sequences related to sums of squares

Formula

Complement of A003995.

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

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. A033461, A276517.

Cf. A001476, A046039, A194768, A194769 for 3rd, 4th, 5th, 6th powers.

Sequence in context: A064472 A276887 A276517 * A097757 A304028 A155152

Adjacent sequences: A001419 A001420 A001421 * A001423 A001424 A001425

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Jeff Adams (jeff.adams(AT)byu.net)

Status

approved