A291828 Numbers k such that k^2 is sum of two positive 7th powers.

16, 2048, 34992, 262144, 1250000, 4478976, 13176688, 33554432, 76527504, 160000000, 276922881, 311794736, 573308928, 1003976272, 1686616064, 2733750000, 4294967296, 6565418768, 9795520512, 14301947824, 20480000000, 28817416656, 35446128768, 39909726208

Offset

1,1

Comments

When a^7 + b^7 = m, (ma)^7 + (mb)^7 = m^8 is square.

When k in this sequence, k*(n^7) (n = 2, 3, ... ) is also in this sequence.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..447

Example

16^2 = 2^8 = 2^7 + 2^7, so 16 is in the sequence.
276922881^2 = 129^7 + 358^7, so 276922881 is in the sequence.

Mathematica

lst={}; Do[If[IntegerQ[(n^2-a^7)^(1/7)], AppendTo[lst, n]], {n, 4*10^10}, {a, (n^2/2)^(1/7)}]; lst

Crossrefs

Cf. A000290, A001015, A004431, A050801.

Sequence in context: A265213 A176886 A159389 * A086804 A317450 A121366

Adjacent sequences: A291825 A291826 A291827 * A291829 A291830 A291831

Keyword

nonn

Author

XU Pingya, Sep 03 2017

Status

approved