|
| |
|
|
A293645
|
|
Positive numbers that are the sum of two (possibly negative) coprime cubes.
|
|
4
|
|
|
|
1, 2, 7, 9, 19, 26, 28, 35, 37, 61, 63, 65, 91, 98, 117, 124, 126, 127, 133, 152, 169, 189, 215, 217, 218, 271, 279, 316, 331, 335, 341, 342, 344, 351, 370, 386, 387, 397, 407, 468, 469, 485, 511, 513, 539, 547, 559, 602, 604, 631, 637, 657, 665, 721, 728, 730
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Also sum or difference of two coprime cubes. - David A. Corneth, Oct 20 2017
|
|
|
LINKS
|
David A. Corneth, Table of n, a(n) for n = 1..10000, (first 101 terms from Rosalie Fay).
|
|
|
EXAMPLE
|
19 = 3^3 + (-2)^3, where 3 and -2 are coprime, so 19 is in the sequence.
152 = 5^3 + 3^3, where 5 and 3 are coprime, so 152 is in the sequence.
|
|
|
MAPLE
|
filter:= proc(n) local s, x, y;
for s in numtheory:-divisors(n) do
x:= s/2 + sqrt(12*n/s-3*s^2)/6;
if not x::integer then next fi;
y:= s - x;
if igcd(x, y) = 1 then return true fi;
od;
false
end proc:
select(filter, [seq(seq(9*i+j, j=[1, 2, 7, 8, 9]), i=0..1000)]); # Robert Israel, Oct 22 2017
|
|
|
PROG
|
(PARI) upto(lim) = {my(res = List([2]), c, i, j); for(i=1, sqrtnint(lim, 3), for(j=0, sqrtnint(lim - i^3, 3), if(gcd(i, j) == 1, listput(res, c)))); for(i=1, sqrtint(lim\3)+1, for(j = 1, i, if(gcd(i, j) == 1, c = i^3 - (i-j)^3; if(c<=lim, listput(res, c), next(2))))); listsort(res, 1); res} \\ David A. Corneth, Oct 20 2017
|
|
|
CROSSREFS
|
Cf. A003325 (positive cubes); A020895 (cubefree); A293646 (only coprime); A293647, A293650.
Sequence in context: A055673 A177737 A336770 * A293646 A020895 A174247
Adjacent sequences: A293642 A293643 A293644 * A293646 A293647 A293648
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Rosalie Fay, Oct 16 2017
|
|
|
STATUS
|
approved
|
| |
|
|
