A291852 Numbers k such that k^4 is the sum of two positive 5th powers.

16, 512, 3888, 16384, 50000, 124416, 268912, 524288, 944784, 1185921, 1600000, 2576816, 3981312, 5940688, 8605184, 12150000, 16777216, 22717712, 30233088, 37949472, 39617584, 51200000, 65345616, 82458112, 102981488, 127401984, 156250000, 190102016, 229582512

Offset

1,1

Comments

When a^5 + b^5 = m, (m^3 * a)^5 + (m^3 * b)^5 = m^16 is 4th power.

When k in this sequence, k * (n^5), for n > 1, is also in this sequence.

Links

Table of n, a(n) for n=1..29.

Example

16^4 = 8^5 + 8^5, so 16 is in the sequence.
1185921^4 = 35937^5 + 71874^5, so 1185921 is in the sequence.

Mathematica

lst={}; Do[If[IntegerQ[(n^4-a^5)^(1/5)], AppendTo[lst, n]], {n, 2.3*10^8}, {a, (n^4/2)^(1/5)}]; lst

Crossrefs

Cf. A000583, A000584, A000404, A009003, A050801.

Sequence in context: A250400 A214624 A322888 * A301845 A302269 A302968

Adjacent sequences: A291849 A291850 A291851 * A291853 A291854 A291855

Keyword

nonn

Author

XU Pingya, Sep 04 2017

Status

approved