A291826 Numbers k such that k^5 is sum of 2 nonzero 6th powers.

32, 2048, 23328, 131072, 500000, 1492992, 3764768, 8388608, 17006112, 32000000, 56689952, 95551488, 154457888, 240945152, 364500000, 536870912, 772402208, 1088391168, 1160290625, 1505468192, 2048000000, 2744515872, 3628156928, 4737148448, 6115295232

Offset: 1

Author

XU Pingya, Sep 03 2017

Keywords

• nonn

Comments

If a^6 + b^6 = m, then (m^4*a)^6 + (m^4*b)^6 = m^25 = (m^5)^5 is 5th power. Therefore A003358(n)^5 is a term of this sequence for all n.

When k in this sequence, k*(n^6) (n >= 2) is also in this sequence.

If h = (i^6)*(j^6 + 1)^5 for (i >= 1 and j >= 1), then h is in this sequence. It appears that this equation generates all terms of the sequence. - Kieran Bhaskara, Aug 03 2019

Examples

			32^5 = 16^6 + 16^6, so 32 is in the sequence.
1160290625^5 = 17850625^6 + 35701250^6, so 1160290625 is in the sequence.
		

Crossrefs

Cf. A000404, A004431, A003325, A050801, A003336, A003347, A003358.

Programs

Mathematica

lst={};Do[If[IntegerQ[(n^5-a^6)^(1/6)],AppendTo[lst,n]],{n,7*10^9},{a,(n^5/2)^(1/6)}]; lst