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A334964 Numbers that are the sum of three coprime positive cubes.

%I A334964 #22 Jul 23 2025 16:01:59
%S A334964 3,10,17,29,36,43,55,62,66,73,92,99,118,127,129,134,141,153,155,160,
%T A334964 179,190,197,216,218,225,244,251,253,258,277,281,307,314,342,345,349,
%U A334964 352,359,368,371,378,397,405,408,415,433,434,466,469,471,476,495,514,521,532,540,547,557,560,566,567
%N A334964 Numbers that are the sum of three coprime positive cubes.
%C A334964 The greatest common divisor of the three cubes must be 1, but they need not be pairwise coprime.
%H A334964 Robert Israel, <a href="/A334964/b334964.txt">Table of n, a(n) for n = 1..10000</a>
%H A334964 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%e A334964 a(3)=17 is in the sequence because 17 = 1^3 + 2^3 + 2^3 with gcd(1,2,2)=1.
%p A334964 N:= 1000: # for all terms <= N
%p A334964 S:= {seq(seq(seq(x^3+y^3+z^3, z=select(t -> igcd(x,y,t)=1, [$y..floor((N-x^3-y^3)^(1/3))])), y=x..floor(((N-x^3)/2)^(1/3))), x=1..floor((N/3)^(1/3)))}:
%p A334964 sort(convert(S, list));
%o A334964 (PARI) list(lim)=my(v=List(),s,g,x3); lim\=1; if(lim<3, return([])); for(x=1,sqrtnint(lim\3,3), x3=x^3; for(y=x,sqrtnint((lim-x3)\2,3), s=x3+y^3; g=gcd(x,y); if(g>1, for(z=y,sqrtnint(lim-s,3), if(gcd(g,z)==1, listput(v,s+z^3))), for(z=y,sqrtnint(lim-s,3), listput(v,s+z^3))))); Set(v) \\ _Charles R Greathouse IV_, May 18 2020
%Y A334964 Cf. A202679.
%K A334964 nonn
%O A334964 1,1
%A A334964 _Robert Israel_, May 17 2020