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 1-3 of 3 results.

A024975 Sums of three distinct positive cubes.

Original entry on oeis.org

36, 73, 92, 99, 134, 153, 160, 190, 197, 216, 225, 244, 251, 281, 288, 307, 342, 349, 352, 368, 371, 378, 405, 408, 415, 434, 469, 476, 495, 521, 532, 540, 547, 560, 567, 577, 584, 586, 603, 623, 638, 645, 664, 684, 701, 729, 736, 738, 755, 757, 764, 792, 794, 801, 820
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Subsequence of A003072. Equals A024973 if duplicates of repeated entries are removed. - R. J. Mathar, Apr 13 2008

Links

Crossrefs

Cf. A122723 (primes in here), A025399-A025402, A025411 (4 distinct positive cubes).

Programs

  • Mathematica
    Total/@Subsets[Range[10]^3,{3}]//Union (* Harvey P. Dale, Aug 22 2021 *)
  • PARI
    list(lim)=my(v=List(),x3,t); lim\=1; for(x=3,sqrtnint(lim-9,3), x3=x^3; for(y=2,min(x-1,sqrtnint(lim-x3-1,3)), t=x3+y^3; for(z=1,min(y-1,sqrtnint(lim-t,3)), listput(v,t+z^3)))); Set(v) \\ Charles R Greathouse IV, Sep 20 2016

Formula

{n: A025469(n) >= 1}. - R. J. Mathar, Jun 15 2018

Extensions

Verified by Don Reble, Nov 19 2006

A025399 Numbers that are the sum of 3 distinct positive cubes in exactly 1 way.

Original entry on oeis.org

36, 73, 92, 99, 134, 153, 160, 190, 197, 216, 225, 244, 251, 281, 288, 307, 342, 349, 352, 368, 371, 378, 405, 408, 415, 434, 469, 476, 495, 521, 532, 540, 547, 560, 567, 577, 584, 586, 603, 623, 638, 645, 664, 684, 701, 729, 736, 738, 755, 757, 764, 792, 794, 801, 820
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A025395 (not necessarily distinct), A024973.

Programs

  • Mathematica
    Reap[For[n = 1, n <= 1000, n++, pr = Select[ PowersRepresentations[n, 3, 3], Times @@ # != 0 && Length[#] == Length[Union[#]] &]; If[pr != {} && Length[pr] == 1, Print[n, pr]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jul 31 2013 *)

Formula

A024975 MINUS A024974. - R. J. Mathar, May 28 2008
{n: A025469(n) = 1}. - R. J. Mathar, Jun 15 2018

A165454 Numbers the squares of which are sums of three distinct positive cubes.

Original entry on oeis.org

6, 15, 27, 48, 53, 59, 71, 78, 84, 87, 90, 96, 98, 116, 120, 121, 125, 134, 153, 162, 163, 167, 180, 188, 204, 213, 216, 224, 225, 226, 230, 240, 242, 244, 251, 253, 255, 262, 264, 280, 287, 288, 303, 314, 324, 330, 342, 350, 356, 363, 368, 372, 381, 384, 393
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Sep 20 2009

Keywords

Examples

			6 is in the sequence because 6^2 = 1^3+2^3+3^3.
15 is in the sequence because 15^2 = 1^3+2^3+6^3.

Links

Crossrefs

Cf. A161992, A024973, A025399

Programs

  • Maple
    N:= 1000: # to get all terms <= N
sc:= {seq(seq(seq(a^3 + b^3 + c^3, a = 1 .. min(b-1, floor((N^2 - b^3 - c^3)^(1/3)))), b = 2 .. min(c-1,floor((N^2 - c^3)^(1/3)))), c = 3 .. floor(N^(2/3)))}:
select(t -> member(t^2,sc), [$1..N]); # Robert Israel, Jan 27 2015
  • Mathematica
    lst={};Do[Do[Do[d=Sqrt[a^3+b^3+c^3];If[d<=834&&IntegerQ[d],AppendTo[lst, d]],{c,b+1,5!,1}],{b,a+1,5!,1}],{a,5!}];Take[Union@lst,123]
Sqrt[# ]&/@Select[Total/@Subsets[Range[50]^3,{3}],IntegerQ[Sqrt[#]]&]// Union (* Harvey P. Dale, Oct 14 2020 *)

Formula

{k >0: k^2 in A024975}. [R. J. Mathar, Oct 06 2009]

Extensions

Comments moved to the examples by R. J. Mathar, Oct 07 2009
Title corrected by Jeppe Stig Nielsen, Jan 26 2015
Showing 1-3 of 3 results.

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