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A291829
Numbers k such that k^3 is the sum of two positive 7th powers.
0
32, 4096, 69984, 524288, 2500000, 8957952, 26353376, 67108864, 153055008, 320000000, 623589472, 1146617856, 2007952544, 3373232128, 5467500000, 8589934592, 13130837536, 19591041024, 28603895648, 35723051649, 40960000000, 57634833312, 79819452416, 108954414304
OFFSET
1,1
COMMENTS
When a^7 + b^7 = m, (m^2*a)^7 + (m^2*b)^7 = m^15 is a cube.
When k in this sequence, k*(n^7) (n = 2, 3, ... ) is also in this sequence.
EXAMPLE
32^3 = 4^7 + 4^7, so 32 is in the sequence.
35723051649^3 = 16641^7 + 33282^7, so 35723051649 is in the sequence.
MATHEMATICA
lst={}; Do[If[IntegerQ[(n^3-a^7)^(1/7)], AppendTo[lst, n]], {n, 1.467*10^11}, {a, (n^3/2)^(1/7)}]; lst
CROSSREFS
KEYWORD
nonn
AUTHOR
XU Pingya, Sep 03 2017
STATUS
approved