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 1-8 of 8 results.

A025398 Numbers that are the sum of 3 positive cubes in 3 or more ways.

Original entry on oeis.org

5104, 9729, 12104, 12221, 12384, 13896, 14175, 17604, 17928, 19034, 20691, 21412, 21888, 24480, 28792, 29457, 30528, 31221, 32850, 34497, 35216, 36288, 38259, 39339, 39376, 40041, 40060, 40097, 40832, 40851, 41033, 41040, 41364, 41966, 42056, 42687
Offset: 1

Views

Author

David W. Wilson

Keywords

Examples

			a(1) = A230477(3) = 5104 = 1^3 + 12^3 + 15^3 = 2^3 + 10^3 + 16^3 = 9^3 + 10^3 + 15^3. - _Jonathan Sondow_, Oct 24 2013

Links

Crossrefs

Cf. A008917, A018787, A025331, A025397, A025402, A025407, A230477, A343968, A344239.

Programs

  • Mathematica
    Select[ Range[ 50000], 2 < Length @ Cases[ PowersRepresentations[#, 3, 3], {?Positive, ?Positive, A008917%20by%20_Jonathan%20Sondow">?Positive}] &] (* adapted from Alcover's program for A008917 by _Jonathan Sondow, Oct 24 2013 *)
  • PARI
    is(n)=k=ceil((n-2)^(1/3)); d=0; for(a=1,k,for(b=a,k,for(c=b,k,if(a^3+b^3+c^3==n,d++))));d
n=3;while(n<50000,if(is(n)>=3,print1(n,", "));n++) \\ Derek Orr, Aug 27 2015

Formula

A008917(n) < a(n) <= A025397(n). - Jonathan Sondow, Oct 24 2013
{n: A025456(n) >= 3}. - R. J. Mathar, Jun 15 2018

A025396 Numbers that are the sum of 3 positive cubes in exactly 2 ways.

Original entry on oeis.org

251, 1009, 1366, 1457, 1459, 1520, 1730, 1737, 1756, 1763, 1793, 1854, 1945, 2008, 2072, 2241, 2414, 2456, 2458, 2729, 2736, 3060, 3391, 3457, 3592, 3599, 3655, 3745, 3926, 4105, 4112, 4131, 4168, 4229, 4320, 4376, 4402, 4437, 4447, 4473, 4528, 4616
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Subset of A008917; A025397 gives examples of numbers which are in A008917 but not here. - R. J. Mathar, May 28 2008
A025456(a(n)) = 2. - Reinhard Zumkeller, Apr 23 2009
Superset of A024974 . - Christian N. K. Anderson, Apr 11 2013

Examples

			a(1) = 251 = 1^3+5^3+5^3 = 2^3+3^3+6^3. - _Christian N. K. Anderson_, Apr 11 2013

Links

Crossrefs

Cf. A008917, A025322, A025395, A025397, A025404, A343708, A344192.

Programs

  • Mathematica
    Select[Range[5000], Length[DeleteCases[PowersRepresentations[#,3,3], ?(MemberQ[#,0]&)]] == 2&] (* _Harvey P. Dale, Jan 18 2012 *)
  • PARI
    is(n)=k=ceil((n-2)^(1/3)); d=0; for(a=1,k,for(b=a,k,for(c=b,k,if(a^3+b^3+c^3==n,d++))));d
n=3;while(n<5000,if(is(n)==2,print1(n,", "));n++) \\ Derek Orr, Aug 27 2015

A025400 Numbers that are the sum of 3 distinct positive cubes in exactly 2 ways.

Original entry on oeis.org

1009, 1366, 1457, 1520, 1737, 1756, 1793, 1854, 1945, 2072, 2241, 2456, 2736, 3060, 3592, 3599, 3745, 3926, 4105, 4131, 4168, 4229, 4320, 4376, 4437, 4447, 4473, 4616, 4733, 4922, 5130, 5435, 5472, 5643, 5706, 5825, 5832, 6183, 6301, 6642, 6848, 6904
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A025397 (not necessarily distinct)

Programs

  • Mathematica
    Reap[ For[n = 1, n <= 7000, n++, pr = Select[ PowersRepresentations[n, 3, 3], Times @@ # != 0 && Length[#] == Length[Union[#]] &] ; If[pr != {} && Length[pr] == 2, Print[n, pr]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jul 31 2013 *)
Module[{nn=20},Select[Tally[Total/@Subsets[Range[nn]^3,{3}]],#[[2]]==2 && #[[1]]<= nn^3-9&][[All,1]]]//Union (* Harvey P. Dale, Apr 26 2020 *)

Formula

{n: A025469(n) = 2}. - R. J. Mathar, Jun 15 2018

A343969 Numbers that are the sum of three positive cubes in exactly 4 ways.

Original entry on oeis.org

13896, 40041, 44946, 52200, 53136, 58995, 76168, 82278, 93339, 94184, 105552, 110683, 111168, 112384, 112832, 113400, 143424, 149416, 149904, 167616, 169560, 171296, 175104, 196776, 197569, 208144, 216126, 221696, 222984, 224505, 235808, 240813, 252062, 255312, 262781, 266031, 281728, 291213
Offset: 1

Views

Author

David Consiglio, Jr., May 05 2021

Keywords

Comments

Differs from A343968 at term 20 because 161568 = 2^3 + 16^3 + 54^3 = 9^3 + 15^3 + 54^3 = 17^3 + 39^3 + 46^3 = 18^3 + 19^3 + 53^3 = 26^3 + 36^3 + 46^3.

Examples

			44946 is a term because 44946 = 7^3 + 12^3 + 35^3 = 9^3 + 17^3 + 34^3 = 11^3 + 24^3 + 31^3 = 16^3 + 17^3 + 33^3.

Links

Crossrefs

Cf. A025324, A025397, A343968, A343970, A343972, A344278, A345865.

Programs

  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1,50)]
for pos in cwr(power_terms,3):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v == 4])
for x in range(len(rets)):
    print(rets[x])

A344240 Numbers that are the sum of three fourth powers in exactly three ways.

Original entry on oeis.org

811538, 1733522, 2798978, 3750578, 4614722, 6573938, 7303842, 8878898, 12771458, 12984608, 13760258, 14677362, 15601698, 16196193, 17868242, 21556178, 22349522, 25190802, 25589858, 27736352, 29969282, 41532498, 44048498, 44783648, 45182018, 50944418, 54894242, 57052562, 59165442, 60009248
Offset: 1

Views

Author

David Consiglio, Jr., May 12 2021

Keywords

Comments

Differs from A344239 at term 6 because 5978882 = 3^4 + 40^4 + 43^4 = 8^4 + 37^4 + 45^4 = 15^4 + 32^4 + 47^4 = 23^4 + 25^4 + 48^4

Examples

			2798978 is a member of this sequence because 2798978 = 6^4 + 31^4 + 37^4 = 9^4 + 29^4 + 38^4 = 13^4 + 26^4 + 39^4

Links

Crossrefs

Cf. A025397, A344192, A344239, A344242, A344278.

Programs

  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1,50)]
for pos in cwr(power_terms,3):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v == 3])
for x in range(len(rets)):
    print(rets[x])

A025405 Numbers that are the sum of 4 positive cubes in exactly 3 ways.

Original entry on oeis.org

1225, 1521, 1582, 1584, 1738, 1764, 2009, 2249, 2366, 2415, 2422, 2457, 2459, 2485, 2520, 2539, 2753, 2763, 2790, 2799, 3008, 3094, 3185, 3187, 3213, 3248, 3276, 3392, 3456, 3458, 3465, 3572, 3582, 3600, 3607, 3626, 3656, 3717, 3736, 3753, 3815, 3941
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A025359, A025397, A025404, A025407, A343705, A343972, A344242.

Formula

{n: A025457(n) = 3}. - R. J. Mathar, Jun 15 2018

A344804 Numbers that are the sum of two cubes in exactly three ways.

Original entry on oeis.org

87539319, 119824488, 143604279, 175959000, 327763000, 700314552, 804360375, 958595904, 1148834232, 1407672000, 1840667192, 1915865217, 2363561613, 2622104000, 3080802816, 3235261176, 3499524728, 3623721192, 3877315533, 4750893000, 5544709352, 5602516416
Offset: 1

Views

Author

Sean A. Irvine, Jun 14 2021

Keywords

Examples

			87539319 is a term because 87539319 = 167^3 + 436^3 = 22^3 + 423^3 = 255^3 + 414^3 (3 representations).
6963472309248 is not a term because 6963472309248 = 2421^3 + 19083^3 = 5436^3 + 18948^3 = 10200^3 + 18072^3 = 13322^3 + 16630^3 (4 representations).  This is the first difference between this sequence and A018787.

Links

Crossrefs

Cf. A018787, A025286, A025397, A343708, A345865.

A025401 Numbers that are the sum of 3 distinct positive cubes in exactly 3 ways.

Original entry on oeis.org

5104, 9729, 12104, 12384, 14175, 17604, 17928, 20691, 21412, 21888, 24480, 28792, 29457, 30528, 31221, 32850, 34497, 36288, 38259, 39339, 39376, 40060, 40097, 40832, 40851, 41033, 41040, 41364, 42056, 43408, 45144, 46593, 46684, 46747, 46808, 47683
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A025397 (not necessarily distinct)

Programs

  • Mathematica
    Reap[For[n = 1, n <= 50000, n++, pr = Select[ PowersRepresentations[n, 3, 3], Times @@ # != 0 && Length[#] == Length[Union[#]] &]; If[pr != {} && Length[pr] == 3, Print[n, pr]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jul 31 2013 *)

Formula

{n: A025469(n) = 3}. - R. J. Mathar, Jun 15 2018
Showing 1-8 of 8 results.

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

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