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
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
KEYWORD
nonn
AUTHOR
XU Pingya, Sep 03 2017
STATUS
approved