A025399 -id:A025399 - 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

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

A025403 Numbers that are the sum of 4 positive cubes in exactly 1 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, 224, 226, 233, 240, 243, 245, 254, 256, 261, 266, 271, 280

Offset: 1

David W. Wilson

nonn

Eric Weisstein's World of Mathematics, Cubic Number.

Cf. A003327, A025357, A025395, A025399, A025404, A048926, A344189.

Reap[For[n = 1, n <= 300, n++, pr = Select[ PowersRepresentations[n, 4, 3], Times @@ # != 0 &]; If[pr != {} && Length[pr] == 1, Print[n, pr]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jul 31 2013 *)

{n: A025457(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

Vladimir Joseph Stephan Orlovsky, Sep 20 2009

nonn

			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.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A161992, A024973, A025399

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

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 *)

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

Comments moved to the examples by R. J. Mathar, Oct 07 2009

Title corrected by Jeppe Stig Nielsen, Jan 26 2015

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A024975 Sums of three distinct positive cubes.

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

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A025403 Numbers that are the sum of 4 positive cubes in exactly 1 way.

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

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