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

1,1

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.

Links

Table of n, a(n) for n=1..25.

Example

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

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

Crossrefs

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

Sequence in context: A176367 A298669 A007117 * A085533 A360773 A122067

Adjacent sequences: A291828 A291829 A291830 * A291832 A291833 A291834

Keyword

nonn

Author

XU Pingya, Sep 03 2017

Status

approved