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.

A003327 Numbers that are the sum of 4 positive cubes in 1 or more way.

Original entry on oeis.org

4, 11, 18, 25, 30, 32, 37, 44, 51, 56, 63, 67, 70, 74, 81, 82, 88, 89, 93, 100, 107, 108, 119, 126, 128, 130, 135, 137, 142, 144, 145, 149, 154, 156, 161, 163, 168, 180, 182, 187, 191, 193, 198, 200, 205, 206, 217, 219, 224, 226, 233, 240, 243, 245, 252, 254
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

It is conjectured that every number greater than 7373170279850 is in this sequence. [See the paper of the same name. - T. D. Noe, May 25 2017] - Charles R Greathouse IV, Jan 14 2017
As the order of addition doesn't matter we can assume terms are in increasing order. - David A. Corneth, Aug 01 2020

Examples

			From _David A. Corneth_, Aug 01 2020: (Start)
3888 is in the sequence as 3888 = 6^3 + 6^3 + 12^3 + 12^3.
7729 is in the sequence as 7729 = 2^3 + 4^3 + 14^3 + 17^3.
7875 is in the sequence as 7875 = 5^3 + 10^3 + 15^3 + 15^3. (End)

Links

Crossrefs

Cf. A025403, A057905 (complement), A025411 (distinct).
A###### (x, y): Numbers that are the form of x nonzero y-th powers.
Cf. A000404 (2, 2), A000408 (3, 2), A000414 (4, 2), A003072 (3, 3), A003325 (3, 2), A003327 (4, 3), A003328 (5, 3), A003329 (6, 3), A003330 (7, 3), A003331 (8, 3), A003332 (9, 3), A003333 (10, 3), A003334 (11, 3), A003335 (12, 3), A003336 (2, 4), A003337 (3, 4), A003338 (4, 4), A003339 (5, 4), A003340 (6, 4), A003341 (7, 4), A003342 (8, 4), A003343 (9, 4), A003344 (10, 4), A003345 (11, 4), A003346 (12, 4), A003347 (2, 5), A003348 (3, 5), A003349 (4, 5), A003350 (5, 5), A003351 (6, 5), A003352 (7, 5), A003353 (8, 5), A003354 (9, 5), A003355 (10, 5), A003356 (11, 5), A003357 (12, 5), A003358 (2, 6), A003359 (3, 6), A003360 (4, 6), A003361 (5, 6), A003362 (6, 6), A003363 (7, 6), A003364 (8, 6), A003365 (9, 6), A003366 (10, 6), A003367 (11, 6), A003368 (12, 6), A003369 (2, 7), A003370 (3, 7), A003371 (4, 7), A003372 (5, 7), A003373 (6, 7), A003374 (7, 7), A003375 (8, 7), A003376 (9, 7), A003377 (10, 7), A003378 (11, 7), A003379 (12, 7), A003380 (2, 8), A003381 (3, 8), A003382 (4, 8), A003383 (5, 8), A003384 (6, 8), A003385 (7, 8), A003387 (9, 8), A003388 (10, 8), A003389 (11, 8), A003390 (12, 8), A003391 (2, 9), A003392 (3, 9), A003393 (4, 9), A003394 (5, 9), A003395 (6, 9), A003396 (7, 9), A003397 (8, 9), A003398 (9, 9), A003399 (10, 9), A004800 (11, 9), A004801 (12, 9), A004802 (2, 10), A004803 (3, 10), A004804 (4, 10), A004805 (5, 10), A004806 (6, 10), A004807 (7, 10), A004808 (8, 10), A004809 (9, 10), A004810 (10, 10), A004811 (11, 10), A004812 (12, 10), A004813 (2, 11), A004814 (3, 11), A004815 (4, 11), A004816 (5, 11), A004817 (6, 11), A004818 (7, 11), A004819 (8, 11), A004820 (9, 11), A004821 (10, 11), A004822 (11, 11), A004823 (12, 11), A047700 (5, 2).

Programs

  • PARI
    list(lim)=my(v=List(),e=1+lim\1,x='x,t); t=sum(i=1,sqrtnint(e-4,3), x^i^3, O(x^e))^4; for(n=4,lim, if(polcoeff(t,n)>0, listput(v,n))); Vec(v) \\ Charles R Greathouse IV, Jan 14 2017

Extensions

More terms from Eric W. Weisstein

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

A025408 Numbers that are the sum of 4 distinct positive cubes in exactly 1 way.

Original entry on oeis.org

100, 161, 198, 217, 224, 252, 289, 308, 315, 350, 369, 376, 379, 406, 413, 416, 432, 435, 442, 477, 496, 503, 533, 540, 548, 559, 568, 585, 587, 594, 604, 611, 624, 631, 646, 650, 665, 672, 685, 692, 702, 709, 711, 728, 737, 748, 756, 763, 765, 793, 800, 802, 819, 821, 828, 854, 861, 863, 864, 880, 882, 883, 889, 890, 917, 919, 920, 926, 927, 945, 946, 954, 973, 980, 981, 988, 1007, 1010, 1017, 1044
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

First differs from A025411 at a(80)=1044. - Ray Chandler, Feb 19 2005.

Programs

  • Mathematica
    Reap[For[n = 1, n <= 1200, n++, pr = Select[ PowersRepresentations[n, 4, 3], Times @@ # != 0 && Length[#] == Length[Union[#]] &]; If[pr != {} && Length[pr] == 1, Print[n, pr]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jul 31 2013 *)

Extensions

More terms from Ray Chandler, Feb 19 2005.
Showing 1-3 of 3 results.

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

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