A291829 Numbers k such that k^3 is the sum of two positive 7th powers.

32, 4096, 69984, 524288, 2500000, 8957952, 26353376, 67108864, 153055008, 320000000, 623589472, 1146617856, 2007952544, 3373232128, 5467500000, 8589934592, 13130837536, 19591041024, 28603895648, 35723051649, 40960000000, 57634833312, 79819452416, 108954414304

Offset: 1

Author

XU Pingya, Sep 03 2017

Keywords

• nonn

Comments

When a^7 + b^7 = m, (m^2*a)^7 + (m^2*b)^7 = m^15 is a cube.

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

Examples

			32^3 = 4^7 + 4^7, so 32 is in the sequence.
35723051649^3 = 16641^7 + 33282^7, so 35723051649 is in the sequence.
		

Crossrefs

Cf. A000578, A001015, A000404, A009003, A050801.

Programs

Mathematica

lst={};Do[If[IntegerQ[(n^3-a^7)^(1/7)],AppendTo[lst,n]],{n,1.467*10^11},{a,(n^3/2)^(1/7)}]; lst