A051386 Numbers whose 4th power is the sum of two positive cubes.

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

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

From Robert Israel, Jun 01 2015: (Start)

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?

(End)

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

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^4-t, Cubes) intersect Cubes)>0, [$1..N]); # Robert Israel, Jun 01 2015

Crossrefs

Cf. A003325, A051387.

Sequence in context: A288484 A011193 A085960 * A003325 A338667 A101420

Adjacent sequences: A051383 A051384 A051385 * A051387 A051388 A051389

Keyword

nonn

Author

Jud McCranie

Status

approved