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

Author

XU Pingya, Sep 04 2017

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

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

Programs

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]