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
Giovanni Resta, Table of n, a(n) for n = 1..549 (terms < 12000)
Mathematics StackExchange, Sum of three perfect cubes is equal to a perfect fourth
Giovanni Resta, Representations of k^4 for k<12000
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
KEYWORD
nonn
AUTHOR
Robert Israel, Mar 03 2020
EXTENSIONS
More terms from Rémy Sigrist, Mar 04 2020
STATUS
approved