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A291849
Numbers k such that k^3 is the sum of two nonzero 4th powers.
0
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.
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
KEYWORD
nonn
AUTHOR
XU Pingya, Sep 04 2017
STATUS
approved