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A273615 Numbers n such that n^4 is the average of two positive cubes while n is not. 1
329, 518, 566, 662, 732, 741, 777, 804, 806, 876, 921, 998, 1029, 1092, 1236, 1238, 1317, 1497, 1526, 1596, 1812, 1862, 1929, 1988, 2181, 2316, 2604, 2632, 2757, 4204, 4396, 4446, 4684, 5068, 5548, 5782, 5838, 5856, 5928, 5982, 6124, 6126, 6216 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If n is the average of two positive cubes, then n^4 is also the average of two positive cubes. So this sequence focuses on the solutions that are not trivial.

LINKS

Robert Israel, Table of n, a(n) for n = 1..502

EXAMPLE

329 is a term because 329 is not the average of two positive cubes while 329^4 = (1833^3 + 2585^3)/2.

MAPLE

Q:=  proc(x) local t;

  for t in select(t -> t^3<=x and 4*t^3 > x and x/t - t^2 mod 3 = 0,

        numtheory:-divisors(x)) do

    if issqr((x/t - t^2)/3)  then return true fi

  od:

  false

end proc:

select(x -> not(Q(x)) and Q(x^4), [$1..10000]); # Robert Israel, May 26 2016

PROG

(PARI) isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));

lista(nn) = for(n=1, nn, if(isA003325(2*n^4) && !isA003325(2*n), print1(n, ", ")));

(PARI) T=thueinit('z^3+1);

isA003325(n)=#select(v->min(v[1], v[2])>0, thue(T, n))>0

is(n)=isA003325(2*n^4) && !isA003325(2*n) \\ Charles R Greathouse IV, May 27 2016

CROSSREFS

Cf. A003325, A051387.

Sequence in context: A278352 A246858 A253054 * A231362 A202010 A265195

Adjacent sequences:  A273612 A273613 A273614 * A273616 A273617 A273618

KEYWORD

nonn

AUTHOR

Altug Alkan, May 26 2016

STATUS

approved

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Last modified May 7 07:37 EDT 2021. Contains 343636 sequences. (Running on oeis4.)