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

3, 10, 17, 29, 36, 43, 55, 62, 66, 73, 92, 99, 118, 127, 129, 134, 141, 153, 155, 160, 179, 190, 197, 216, 218, 225, 244, 251, 253, 258, 277, 281, 307, 314, 342, 345, 349, 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

Offset: 1

Author

Robert Israel, May 17 2020

Keywords

• nonn

Comments

The greatest common divisor of the three cubes must be 1, but they need not be pairwise coprime.

Examples

			a(3)=17 is in the sequence because 17 = 1^3 + 2^3 + 2^3 with gcd(1,2,2)=1.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A202679.

Programs

Maple

N:= 1000: # for all terms <= N
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)))}:
sort(convert(S, list));

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