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

1,1

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

Links

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

Example

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

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

Crossrefs

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

Sequence in context: A239646 A323540 A304123 * A302270 A301846 A302969

Adjacent sequences: A291823 A291824 A291825 * A291827 A291828 A291829

Keyword

nonn

Author

XU Pingya, Sep 03 2017

Status

approved