

A051386


Numbers whose 4th power is the sum of two positive cubes.


3



2, 9, 16, 28, 35, 54, 65, 72, 91, 126, 128, 133, 134, 152, 182, 183, 189, 201, 217, 219, 224, 243, 250, 273, 278, 280, 309, 341, 344, 351, 370, 399, 407, 422, 432, 453, 468, 497, 513, 520, 539, 559, 576, 579, 637, 651, 658, 686, 728, 730, 737, 756, 793, 854
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OFFSET

1,1


COMMENTS

n such that n^4 = r^3 + s^3 has a solution with r>0, s>0.
By multiplying n^4 = r^3 + s^3 by n^3, also numbers whose 7th power is expressible as the sum of positive cubes.
When n is the sum of 2 positive cubes (A003325) there is a trivial solution: e.g., 133 is a term in A003325, 133=2^3+5^3 and 133^4=(2*133)^3+(5*133)^3.  Zak Seidov, Oct 17 2011
Slightly more generally, if x^3 + y^3 = u*v^4, then (u*v*w^3)^4 = (u*w^4*x)^3 + (u*w^4*y)^3, so u*v*w^3 is in the sequence for any w >= 1.
There are at least five pairs of adjacent numbers in the sequence: (133,134),(182,183), (854,855), (1842,1843), (3473,3474). Are there infinitely many?
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LINKS



EXAMPLE

134^4 = 469^3 + 603^3.


MAPLE

N:= 1000: # to get all terms <= N
Cubes:= {seq(x^3, x=1..floor(N^(4/3)))}:
select(n > nops(map(t > n^4t, Cubes) intersect Cubes)>0, [$1..N]); # Robert Israel, Jun 01 2015


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



