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%I #37 Dec 31 2022 14:46:25
%S 3,4,24,32,81,98,108,168,192,228,256,312,375,500,525,588,648,671,784,
%T 847,864,1014,1029,1183,1225,1261,1323,1344,1372,1536,1824,2048,2187,
%U 2496,2646,2888,2916,3000,3549,3993,4000,4200,4225,4536,4563,4644,4704,4914,5054,5184,5324,5368
%N Numbers whose 5th power is expressible as the sum of two positive cubes.
%C 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]
%C The number 3549 is in this sequence but not in A050801, so the two sequences are distinct. - _Eric M. Schmidt_, Oct 29 2013
%H Chai Wah Wu, <a href="/A051394/b051394.txt">Table of n, a(n) for n = 1..1000</a> (terms for n <= 185 from Donovan Johnson)
%e 24^5 = 96^3 + 192^3.
%t 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 *)
%o (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
%Y Cf. A050801.
%K nonn
%O 1,1
%A _Jud McCranie_
%E Sequence corrected and extended by _Jonathan Sondow_, Oct 28 2013
%E Corrected by _Donovan Johnson_, Oct 29 2013
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