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A291830
Numbers k such that k^4 is sum of two positive 7th powers.
0
4, 512, 8748, 16641, 65536, 312500, 1119744, 2130048, 3294172, 4787344, 5359225, 8388608, 19131876, 36393867, 40000000, 77948684, 143327232, 250994068, 268468225, 272646144, 344882041, 421654016, 612780032, 683437500, 685980800, 1073741824, 1300078125
OFFSET
1,1
COMMENTS
When a^7 + b^7 = m, (ma)^7 + (mb)^7 = m^8 is 4th power.
When k in this sequence, k*(n^7) (n = 2, 3, ... ) is also in this sequence.
EXAMPLE
4^4 = 2^7 + 2^7, so 4 is in the sequence.
16641^4 = 129^7 + 358^7, so 16641 is in the sequence.
MATHEMATICA
lst={}; Do[If[IntegerQ[(n^4-a^7)^(1/7)], AppendTo[lst, n]], {n, 1.4*10^9}, {a, (n^4/2)^(1/7)}]; lst
CROSSREFS
KEYWORD
nonn
AUTHOR
XU Pingya, Sep 03 2017
STATUS
approved