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

1,1

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sums of cubes

Example

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

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));

Prog

(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

Crossrefs

Cf. A202679.

Sequence in context: A297665 A309347 A273235 * A309351 A003615 A043293

Adjacent sequences: A334961 A334962 A334963 * A334965 A334966 A334967

Keyword

nonn

Author

Robert Israel, May 17 2020

Status

approved