A025402 -id:A025402 - cp's OEIS frontend

A024975 Sums of three distinct positive cubes.

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

Clark Kimberling

nonn

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

T. D. Noe, Table of n, a(n) for n = 1..10000

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

Total/@Subsets[Range[10]^3,{3}]//Union (* Harvey P. Dale, Aug 22 2021 *)

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

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

Verified by Don Reble, Nov 19 2006

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

David W. Wilson

nonn

			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

Donovan Johnson, Table of n, a(n) for n = 1..10000

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

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 *)

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

A008917(n) < a(n) <= A025397(n). - Jonathan Sondow, Oct 24 2013

{n: A025456(n) >= 3}. - R. J. Mathar, Jun 15 2018

A025469 Number of partitions of n into 3 distinct positive cubes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

David W. Wilson

nonn

In other words, number of solutions to the equation n = x^3 + y^3 + z^3 with x > y > z > 0. - Antti Karttunen, Aug 29 2017

			From _Antti Karttunen_, Aug 29 2017: (Start)
For n = 36 there is one solution: 36 = 27 + 8 + 1, thus a(36) = 1.
For n = 1009 there are two solutions: 1009 = 10^3 + 2^3 + 1^3 = 9^3 + 6^3 + 4^3, thus a(1009) = 2. This is also the first point where sequence attains value greater than one.
(End)

Antti Karttunen, Table of n, a(n) for n = 0..17073
Index entries for sequences related to sums of cubes

Cf. A025465 (not necessarily distinct), A025468, A025419 (greedy inverse).

Cf. A024975 (positions of nonzero terms), A024974 (positions of terms > 1), A025399-A025402.

A025469 := proc(n)
    local a, x, y, zcu ;
    a := 0 ;
    for x from 1 do
        if 3*x^3 > n then
            return a;
        end if;
        for y from x+1 do
            if x^3+2*y^3 > n then
                break;
            end if;
            zcu := n-x^3-y^3 ;
            if zcu > y^3 and isA000578(zcu) then
                a := a+1 ;
            end if;
        end do:
    end do:
end proc:
seq(A025469(n),n=1..80) ; # R. J. Mathar, Jun 15 2018

Table[Count[IntegerPartitions[n, {3}], ?(And[UnsameQ @@ #, AllTrue[#, IntegerQ[#^(1/3)] &]] &)], {n, 105}] (* _Michael De Vlieger, Aug 29 2017 *)

A025469(n) = { my(s=0); for(x=1,n,if(ispower(x,3),for(y=x+1,n-x,if(ispower(y,3),for(z=y+1,n-(x+y),if((ispower(z,3)&&(x+y+z)==n),s++)))))); (s); }; \\ Antti Karttunen, Aug 29 2017

a(n) = A025465(n) - A025468(n). - Antti Karttunen, Aug 29 2017

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

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

nonn

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

Subset of A001239.

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

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
Christian N. K. Anderson, Decomposition of the first 10000 terms into 3 sets of cube triples
Sequences related to sums of squares and cubes

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

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

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A024975 Sums of three distinct positive cubes.

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

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A025469 Number of partitions of n into 3 distinct positive cubes.

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

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