A291830 Numbers k such that k^4 is sum of two positive 7th powers.

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.

Links

Table of n, a(n) for n=1..27.

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

Cf. A000583, A001015, A000404, A009003, A050801.

Sequence in context: A268468 A278878 A348703 * A368370 A003393 A089668

Adjacent sequences: A291827 A291828 A291829 * A291831 A291832 A291833

Keyword

nonn

Author

XU Pingya, Sep 03 2017

Status

approved