OFFSET
1,1
COMMENTS
Every term z of A050801 is a term of this sequence: z^2 = x^3 + y^3, so z^2*z^3 = z^5 = (z*x)^3 + (z*y)^3. Are there any terms that are not in A050801? [Joerg Arndt, Sep 30 2012]
The number 3549 is in this sequence but not in A050801, so the two sequences are distinct. - Eric M. Schmidt, Oct 29 2013
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..1000 (terms for n <= 185 from Donovan Johnson)
EXAMPLE
24^5 = 96^3 + 192^3.
MATHEMATICA
tpcQ[n_]:=Module[{c=PowersRepresentations[n^5, 2, 3]}, FreeQ[Flatten[c], 0]&&Length[c]>0]; Select[Range[2, 900], tpcQ] (* The program generates the first 21 terms of the sequence. *) (* Harvey P. Dale, Dec 31 2022 *)
PROG
(PARI) mm=1645714; cb=vector(mm); for(i=1, mm, cb[i]=i^3); j=2; for(n=2, 5368, p5=n^5; while(cb[j]<p5, j++); j1=1; j2=j; for(m=1, mm, if(j1>j2, next(2)); s=cb[j1]+cb[j2]; if(s<p5, j1++; next, if(s>p5, j2--; next); print1(n ", "); next(2)))) \\ Donovan Johnson, Oct 31 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Sequence corrected and extended by Jonathan Sondow, Oct 28 2013
Corrected by Donovan Johnson, Oct 29 2013
STATUS
approved