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A291852
Numbers k such that k^4 is the sum of two positive 5th powers.
0
16, 512, 3888, 16384, 50000, 124416, 268912, 524288, 944784, 1185921, 1600000, 2576816, 3981312, 5940688, 8605184, 12150000, 16777216, 22717712, 30233088, 37949472, 39617584, 51200000, 65345616, 82458112, 102981488, 127401984, 156250000, 190102016, 229582512
OFFSET
1,1
COMMENTS
When a^5 + b^5 = m, (m^3 * a)^5 + (m^3 * b)^5 = m^16 is 4th power.
When k in this sequence, k * (n^5), for n > 1, is also in this sequence.
EXAMPLE
16^4 = 8^5 + 8^5, so 16 is in the sequence.
1185921^4 = 35937^5 + 71874^5, so 1185921 is in the sequence.
MATHEMATICA
lst={}; Do[If[IntegerQ[(n^4-a^5)^(1/5)], AppendTo[lst, n]], {n, 2.3*10^8}, {a, (n^4/2)^(1/5)}]; lst
CROSSREFS
KEYWORD
nonn
AUTHOR
XU Pingya, Sep 04 2017
STATUS
approved