A180968 -id:A180968 - cp's OEIS frontend

A003334 Numbers that are the sum of 11 positive cubes.

11, 18, 25, 32, 37, 39, 44, 46, 51, 53, 58, 60, 63, 65, 67, 70, 72, 74, 77, 79, 81, 84, 86, 88, 89, 91, 93, 95, 96, 98, 100, 102, 103, 105, 107, 109, 110, 112, 114, 115, 116, 117, 119, 121, 122, 123, 124, 126, 128, 129, 130, 131, 133, 135, 136, 137, 138, 140, 141, 142, 143, 144

Offset: 1

N. J. A. Sloane

As the order of addition doesn't matter we can assume terms are in nondecreasing order. - David A. Corneth, Aug 01 2020

The sequence contains all integers greater than 321 which is the last of only 92 positive integers not in this sequence. - M. F. Hasler, Aug 25 2020

			From _David A. Corneth_, Aug 01 2020: (Start)
1120 is in the sequence as 1120 = 2^3 + 3^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3 + 5^3 +  8^3.
2339 is in the sequence as 2339 = 4^3 + 4^3 + 4^3 + 4^3 + 5^3 + 5^3 + 5^3 + 5^3 + 5^3 + 9^3 +  9^3.
3594 is in the sequence as 3594 = 4^3 + 5^3 + 6^3 + 6^3 + 6^3 + 6^3 + 7^3 + 7^3 + 7^3 + 8^3 + 10^3. (End)

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Other sequences S(k, m) of numbers that are the sum of k nonzero m-th powers:
  A000404 = S(2, 2), A000408 = S(3, 2), A000414 = S(4, 2) complement of A000534,
  A047700 = S(5, 2) complement of A047701, A180968 = complement of S(6,2);
  A003325 = S(2, 3), A003072 = S(3, 3), A003327 .. A003335 = S(4 .. 12, 3) and A332107 .. A332111 = complement of S(7 .. 11, 3);
  A003336 .. A003346 = S(2 .. 12, 4), A003347 .. A003357 = S(2 .. 12, 5),
  A003358 .. A003368 = S(2 .. 12, 6), A003369 .. A003379 = S(2 .. 12, 7),
  A003380 .. A003390 = S(2 .. 12, 8), A003391 .. A004801 = S(2 .. 12, 9),
  A004802 .. A004812 = S(2 .. 12, 10), A004813 .. A004823 = S(2 .. 12, 11).

(A003334_upto(N, k=11, m=3)=[i|i<-[1..#N=sum(n=1, sqrtnint(N, m), 'x^n^m, O('x^N))^k], polcoef(N, i)])(150) \\ See also A003333 for alternate code. - M. F. Hasler, Aug 03 2020

a(n) = n + 92 for all n > 229. - M. F. Hasler, Aug 25 2020

A047701 All positive numbers that are not the sum of 5 nonzero squares.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 9, 10, 12, 15, 18, 33

Offset: 1

Arlin Anderson (starship1(AT)gmail.com)

			4 = 1^2 + 1^2 + 1^2 + 1^2 + 0^2, but the last square is 0, and hence 4 is in the sequence.
5 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2, and therefore 5 is not in the sequence.

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 33, pp 12, Ellipses, Paris 2008.
E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, Theorem 2., p. 73.
Ivan Niven and Herbert S. Zuckerman, An Introduction to the Theory of Numbers, New York: John Wiley (1980), p. 145

Index entries for sequences related to sums of squares

Cf. A047700, A000534, A180968 (not the sum of 6 squares).

Select[ Range[100], Select[ PowersRepresentations[#, 5, 2], FreeQ[#, 0]& ] == {}& ] (* Jean-François Alcover, Sep 03 2013 *)

Name changed. - Wolfdieter Lang, Mar 28 2013

A295796 The only integers that cannot be partitioned into a sum of seven positive squares.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 17, 20

Offset: 1

Robert Price, Nov 27 2017

Dubouis, E.; L'Interm. des math., vol. 18, (1911), pp. 55-56, 224-225.
Grosswald, E.; Representation of Integers as Sums of Squares, Springer-Verlag, New York Inc., (1985), pp.73-74.

Gordon Pall, On Sums of Squares, The American Mathematical Monthly, Vol. 40, No. 1, (January 1933), pp. 10-18.

Cf. A025431, A047701, A180968.

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A003334 Numbers that are the sum of 11 positive cubes.

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A047701 All positive numbers that are not the sum of 5 nonzero squares.

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A295796 The only integers that cannot be partitioned into a sum of seven positive squares.

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