|
%I #22 Aug 07 2019 03:17:10
%S 32,2048,23328,131072,500000,1492992,3764768,8388608,17006112,
%T 32000000,56689952,95551488,154457888,240945152,364500000,536870912,
%U 772402208,1088391168,1160290625,1505468192,2048000000,2744515872,3628156928,4737148448,6115295232
%N Numbers k such that k^5 is sum of 2 nonzero 6th powers.
%C 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.
%C When k in this sequence, k*(n^6) (n >= 2) is also in this sequence.
%C 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
%e 32^5 = 16^6 + 16^6, so 32 is in the sequence.
%e 1160290625^5 = 17850625^6 + 35701250^6, so 1160290625 is in the sequence.
%t lst={};Do[If[IntegerQ[(n^5-a^6)^(1/6)],AppendTo[lst,n]],{n,7*10^9},{a,(n^5/2)^(1/6)}]; lst
%Y Cf. A000404, A004431, A003325, A050801, A003336, A003347, A003358.
%K nonn
%O 1,1
%A _XU Pingya_, Sep 03 2017
|
