A291849 Numbers k such that k^3 is the sum of two nonzero 4th powers.

8, 128, 648, 2048, 4913, 5000, 10368, 19208, 32768, 52488, 78608, 80000, 117128, 165888, 228488, 307328, 397953, 405000, 524288, 551368, 668168, 839808, 912673, 1042568, 1257728, 1280000, 1555848, 1874048, 2238728, 2654208, 3070625, 3125000, 3655808, 4251528

Offset

1,1

Comments

If a^4 + b^4 = m, then (m^2 * a)^4 + (m^2 * b)^4 = m^9 = (m^3)^3 is a cube. Therefore A003336(n)^3 are terms of this sequence.

When k is in this sequence, k(n^4), for n > 1, is also in this sequence.

Links

Table of n, a(n) for n=1..34.

Example

8^3 = 2^9 = 4^4 + 4^4, so 8 is in the sequence.
4913^3 = 17^9 = 17^8 * (1 + 2^4) = 289^4 + 578^4, so 4913 is in the sequence.

Mathematica

fourthPowerFlags = Union@Flatten@Table[a^4 + b^4 && GCD[a, b] == 1, {a, 4}, {b, a, 4}]; Take[Union@Flatten@Table[k^4 * fourthPowerFlags[[j]]^3, {k, 27}, {j, 6}], 34]

Crossrefs

Cf. A000404, A004431, A003325, A050801, A003336, A003347.

Sequence in context: A204194 A093586 A238651 * A301844 A302268 A302967

Adjacent sequences: A291846 A291847 A291848 * A291850 A291851 A291852

Keyword

nonn

Author

XU Pingya, Sep 04 2017

Status

approved