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

Author

XU Pingya, Sep 03 2017

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000290, A001015, A004431, A050801.

Programs

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