|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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.
|
|
LINKS
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|