A291831 Numbers k such that k^5 is sum of two positive 7th powers.

8, 1024, 17496, 131072, 625000, 2146689, 2239488, 6588344, 16777216, 38263752, 80000000, 155897368, 74776192, 86654464, 501988136, 843308032, 1366875000, 2147483648, 3282709384, 4694808843, 4897760256, 7150973912, 10240000000, 10474708672, 12406605875

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 5th power.

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

Examples

			8^5 = 4^7 + 4^7, so 8 is in the sequence.
2146689^5 = 16641^7 + 33282^7, so 2146689 is in the sequence.
		

Crossrefs

Cf. A000584, A001015, A000404, A009003, A050801.

Programs

Mathematica

lst={};Do[If[IntegerQ[(n^5-a^7)^(1/7)],AppendTo[lst,n]],{n,1.3*10^10},{a,(n^5/2)^(1/7)}]; lst