A291851 Numbers k such that k^3 is the sum of two positive 5th powers.

4, 128, 972, 1089, 4096, 12500, 31104, 34848, 59536, 67228, 75625, 131072, 236196, 264627, 400000, 644204, 995328, 1050625, 1115136, 1485172, 1605289, 1905152, 2151296, 2420000, 3037500, 3403125, 4194304, 5679428, 7558272, 8468064, 9771876, 9904396, 9966649

Offset

1,1

Comments

If a^5 + b^5 = m, then (ma)^5 + (mb)^5 = m^6 = (m^2)^3 is a cube. Therefore the square of each term of A003347 is a term of this sequence.

When k is in this sequence, k * (n^5), for n > 1, is also in this sequence.

Links

Table of n, a(n) for n=1..33.

Example

4^3 = 2^6 = 2^5 + 2^5, so 4 is in the sequence.
1089^3 = 33^5 + 66^5, so 1089 is in the sequence.

Mathematica

lst={}; Do[If[IntegerQ[(n^3-a^5)^(1/5)], AppendTo[lst, n]], {n, 10^7}, {a, (n^3/2)^(1/5)}]; lst

Crossrefs

Cf. A000404, A004431, A003325, A050801, A003336, A003347.

Sequence in context: A070781 A152421 A270959 * A128790 A267796 A013823

Adjacent sequences: A291848 A291849 A291850 * A291852 A291853 A291854

Keyword

nonn

Author

XU Pingya, Sep 04 2017

Status

approved