cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-14 of 14 results.

A069136 Numbers that are not the sum of 5 nonnegative cubes.

Original entry on oeis.org

6, 7, 13, 14, 15, 20, 21, 22, 23, 34, 39, 41, 42, 46, 47, 48, 49, 50, 53, 58, 60, 61, 69, 76, 77, 79, 84, 85, 86, 87, 95, 98, 102, 103, 104, 105, 106, 110, 111, 112, 113, 114, 117, 121, 122, 123, 124, 132, 139, 140, 147, 148, 151, 158, 159, 165
Offset: 1

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Author

N. J. A. Sloane, Apr 08 2002

Keywords

Comments

Sequence is conjectured to be finite.
Comment from Richard C. Schroeppel, Sep 22 2010: It is conjectured that 7373170279850 is the largest number requiring more than four cubes (see Deshouillers et al.).

References

  • Bohman, Jan and Froberg, Carl-Erik; Numerical investigation of Waring's problem for cubes, Nordisk Tidskr. Informationsbehandling (BIT) 21 (1981), 118-122.
  • F. Romani, Computations concerning Waring's problem, Calcolo, 19 (1982), 415-431.

Links

Crossrefs

Sums of k cubes, number of ways of writing n as, for k=1..9: A010057, A173677, A051343, A173678, A173679, A173680, A173676, A173681, A173682.

A219329 Numbers that can be expressed as the sum of three nonnegative cubes in three ways.

Original entry on oeis.org

5104, 5832, 9288, 9729, 10261, 10773, 12104, 12221, 12384, 14175, 17604, 17928, 19034, 20691, 21412, 21888, 24416, 24480, 28792, 29457, 30528, 31221, 32850, 34497, 35216, 36288, 38259, 39339, 39376, 39528, 40060, 40097, 40832, 40851, 41033, 41040, 41364
Offset: 1

Views

Author

Kevin L. Schwartz and Christian N. K. Anderson, Apr 11 2013

Keywords

Comments

Index of A051343 = 9, superset of index of A025456 = 3.
Subset of A001239.

Examples

			a(1) = 5104 = 1^3+12^3+15^3 = 2^3+10^3+16^3 = 9^3+10^3+15^3.

Links

Crossrefs

Other sums of cubes: A025402, A025398, A024974, A001239, A008917.
Cf. A025456, A051343.
Cf. A025396.

Programs

  • Mathematica
    Select[Range[42000],Length[PowersRepresentations[#,3,3]]==3&] (* Harvey P. Dale, Sep 28 2016 *)

A363777 Expansion of 1/(Sum_{k>=0} x^(k^3))^3.

Original entry on oeis.org

1, -3, 6, -10, 15, -21, 28, -36, 42, -43, 36, -18, -14, 63, -132, 224, -336, 459, -578, 672, -714, 671, -504, 168, 378, -1161, 2184, -3419, 4794, -6183, 7396, -8169, 8169, -7014, 4308, 321, -7156, 16311, -27636, 40607, -54222, 66924, -76572, 80451, -75372, 57883
Offset: 0

Views

Author

Seiichi Manyama, Jun 21 2023

Keywords

Crossrefs

Convolution inverse of A051343.
Column k=3 of A363779.
Cf. A363783.

Programs

  • PARI
    my(N=50, x='x+O('x^N)); Vec(1/sum(k=0, N^(1/3), x^k^3)^3)

Formula

a(0) = 1; a(n) = -(3/n) * Sum_{k=1..n} A363783(k) * a(n-k).

A286351 a(n) is the number of decompositions of 2^(n-1)*(2^n-1) into 3 nonnegative cubes.

Original entry on oeis.org

0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 6, 3, 0, 1, 1, 3, 0, 4, 1, 2, 1, 2, 2, 8, 0, 0, 0, 7, 3, 10, 1, 4, 1, 2, 3, 2
Offset: 1

Views

Author

Michel Marcus, May 08 2017

Keywords

Comments

From Giovanni Resta, May 09 2017: (Start)
The triples corresponding to n<=40 are reported in the cited paper. Those corresponding to a(41)-a(43) are:
41: (1806336, 90370048, 118874112), (9340200, 89678370, 119250526);
42: (24663948, 61547632, 211219316), (37015132, 42806240, 188598692), (94126080, 154352128, 172803584);
43: (16384, 266321920, 270516224), (94478388, 245170170, 284820886).
(End)

Links

Crossrefs

Cf. A006516, A051343.

Programs

  • Mathematica
    Table[Length@ PowersRepresentations[2^(n - 1) (2^n - 1), 3, 3] - Boole[n == 1], {n, 17}] (* Michael De Vlieger, May 08 2017 *)

Extensions

a(41)-a(43) from Giovanni Resta, May 09 2017
Previous Showing 11-14 of 14 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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