A291832 Numbers k such that k^6 is sum of two positive 7th powers.

64, 8192, 139968, 1048576, 5000000, 17915904, 52706752, 134217728, 306110016, 640000000, 1247178944, 2293235712, 4015905088, 6746464256, 10935000000, 17179869184, 26261675072, 39182082048, 57207791296, 81920000000, 115269666624, 159638904832, 217908828608

Offset: 1

Author

XU Pingya, Sep 03 2017

Keywords

• nonn

Comments

When a^7 + b^7 = m, (m^5*a)^7 + (m^5*b)^7 = m^36 is 6th power.

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

Examples

			64^6 = 32^7 + 32^7, so 64 is in the sequence.
(5000000)^6 = (500000)^7 + (500000)^7, so 5000000 is in the sequence.
		

Crossrefs

Cf. A001014, A001015, A000404, A009003, A050801.

Programs

Mathematica

lst={};Do[If[IntegerQ[(n^6-a^7)^(1/7)],AppendTo[lst,n]],{n,2.9*10^11},{a,(n^6/2)^(1/7)}]; lst