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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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A024975.

Sequence in context: A063480 A305026 A009633 * A156333 A116281 A168530

Adjacent sequences:  A327583 A327584 A327585 * A327587 A327588 A327589

KEYWORD

nonn

AUTHOR

Robert Israel, Mar 03 2020

EXTENSIONS

More terms from Rémy Sigrist, Mar 04 2020

STATUS

approved

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Last modified December 1 02:46 EST 2021. Contains 349426 sequences. (Running on oeis4.)