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.

Showing 1-4 of 4 results.

A135693 Not the sum of three positive squares or cubes.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 15, 23, 31, 87, 111, 119, 148, 167, 263, 311, 335, 391, 407, 455, 559, 599, 839, 951, 1159, 1231, 1287, 1303, 1391, 1455, 1463, 1607, 1660, 1679, 1751, 1863, 1991, 2351, 2615, 2799, 3247, 3983, 4327, 4367, 5199, 5655, 6047, 6159, 6351
Offset: 1

Views

Author

Zak Seidov and Giovanni Resta, Feb 24 2008

Keywords

Comments

No other terms < 10^9. Presumably the sequence is finite.
Sum can include a mix of squares and cubes. - James C. McMahon, Apr 19 2025

Links

Crossrefs

Cf. A113505, A135367.
Cf. A004214, A057904.

Programs

  • Mathematica
    lim=40000; s=Range[Sqrt[lim]]^2; c=Range[Surd[lim, 3]]^3; A135693=Complement[Range[lim], Select[Total/@Tuples[Union[s, c], {3}], #<=lim&]] (* James C. McMahon, Apr 19 2025 *)

Extensions

Edited by N. J. A. Sloane, Mar 01 2008

A135402 Not the sum of three squares or cubes greater than 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 18, 19, 23, 30, 31, 46, 55, 64, 87, 91, 111, 119, 128, 130, 148, 151, 167, 263, 311, 335, 391, 407, 455, 487, 540, 559, 599, 839, 951, 967, 1159, 1231, 1287, 1303, 1391, 1455, 1463, 1607, 1660, 1679, 1751
Offset: 1

Views

Author

Giovanni Resta, Feb 24 2008

Keywords

Links

Crossrefs

Cf. A113505, A135693, A135367, A135393.

A135393 Not the sum of three perfect powers greater than 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 18, 19, 23, 30, 31, 46, 55, 87, 111, 119, 151, 167, 335, 1391, 1455, 1607, 1679, 1991, 25887, 26375
Offset: 1

Views

Author

Giovanni Resta, Feb 24 2008

Keywords

Comments

Probably there are no further terms.

Crossrefs

Cf. A113505, A135693, A135367, A135402.

A187054 Numbers that are not the sum of three powerful numbers (A001694).

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 15, 23, 31, 87, 111, 119
Offset: 1

Views

Author

Charles R Greathouse IV, Mar 02 2011

Keywords

Comments

Heath-Brown shows that this sequence is finite, resolving a conjecture of Erdos. Presumably a(12) = 119 is the last term.

References

  • D. R. Heath-Brown, "Sums of three square-full numbers". Number theory, Vol. I (Budapest, 1987), pp. 163-171, Colloq. Math. Soc. János Bolyai, 51, North-Holland, Amsterdam, 1990.
  • D. R. Heath-Brown, "Ternary quadratic forms and sums of three square-full numbers". Séminaire de Théorie des Nombres, Paris 1986-87, pp. 137-163, Progr. Math., 75, Birkhäuser Boston, Boston, MA, 1988.

Links

Crossrefs

Proper subsequence of A135367.
Cf. A076871, A135693.

Programs

  • Mathematica
    powerfulQ[n_] := n == 1 || Min[Last /@ FactorInteger[n]] > 1; nn = 1000; pow = Select[Range[nn], powerfulQ]; Complement[Range[nn], Select[Union[Flatten[Outer[Plus, pow, pow, pow]]], # <= nn &]] (* T. D. Noe, Mar 02 2011 *)
Showing 1-4 of 4 results.

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

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