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

Author

XU Pingya, Sep 04 2017

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

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