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A327586
Numbers k such that k^4 = a^3 + b^3 + c^3 for some pairwise coprime positive integers a,b,c.
3
39, 57, 70, 74, 106, 111, 147, 174, 209, 216, 236, 237, 244, 252, 291, 300, 318, 327, 333, 336, 342, 360, 366, 372, 387, 403, 417, 424, 450, 462, 489, 524, 540, 561, 582, 594, 615, 624, 636, 638, 651, 660, 673, 696, 700, 714, 739, 741, 768, 771, 804, 827, 837
OFFSET
1,1
COMMENTS
a(10) = 216 is the least term whose fourth power has two representations as a sum of the cubes of three pairwise coprime positive integers: 216^4 = 1217^3 + 639^3 + 484^3 = 1257^3 + 575^3 + 82^3. - Rémy Sigrist, Mar 04 2020
The least terms with 3 and 4 representations are a(230)=4914 and a(269)=5832, respectively. - Giovanni Resta, Mar 04 2020
LINKS
EXAMPLE
a(3) = 70 is a term because 70^4 = 81^3 + 167^3 + 266^3, and 81, 167 and 266 are positive and pairwise coprime.
MAPLE
N:= 200: # to get all terms <= N
qmax:= N^4: Res:= {}:
for a from 1 while a^3 < qmax do
for b from a+1 while a^3 + b^3 < qmax do
if igcd(a, b) <> 1 then next fi;
for c from b+1 while a^3 + b^3 + c^3 <= qmax do
if igcd(c, a*b) <> 1 then next fi;
q:= a^3 + b^3 + c^3;
if issqr(q) and issqr(sqrt(q)) then
Res:= Res union {sqrt(sqrt(q))};
fi
od od od:
sort(convert(Res, list));
CROSSREFS
Cf. A024975.
Sequence in context: A063480 A305026 A009633 * A156333 A116281 A168530
KEYWORD
nonn
AUTHOR
Robert Israel, Mar 03 2020
EXTENSIONS
More terms from Rémy Sigrist, Mar 04 2020
STATUS
approved