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A291831
Numbers k such that k^5 is sum of two positive 7th powers.
0
8, 1024, 17496, 131072, 625000, 2146689, 2239488, 6588344, 16777216, 38263752, 80000000, 155897368, 74776192, 86654464, 501988136, 843308032, 1366875000, 2147483648, 3282709384, 4694808843, 4897760256, 7150973912, 10240000000, 10474708672, 12406605875
OFFSET
1,1
COMMENTS
When a^7 + b^7 = m, (m^2*a)^7 + (m^2*b)^7 = m^15 is 5th power.
When k in this sequence, k*(n^7) (n = 2, 3, ... ) is also in this sequence.
EXAMPLE
8^5 = 4^7 + 4^7, so 8 is in the sequence.
2146689^5 = 16641^7 + 33282^7, so 2146689 is in the sequence.
MATHEMATICA
lst={}; Do[If[IntegerQ[(n^5-a^7)^(1/7)], AppendTo[lst, n]], {n, 1.3*10^10}, {a, (n^5/2)^(1/7)}]; lst
CROSSREFS
KEYWORD
nonn
AUTHOR
XU Pingya, Sep 03 2017
STATUS
approved