A051394 Numbers whose 5th power is expressible as the sum of two positive cubes.

3, 4, 24, 32, 81, 98, 108, 168, 192, 228, 256, 312, 375, 500, 525, 588, 648, 671, 784, 847, 864, 1014, 1029, 1183, 1225, 1261, 1323, 1344, 1372, 1536, 1824, 2048, 2187, 2496, 2646, 2888, 2916, 3000, 3549, 3993, 4000, 4200, 4225, 4536, 4563, 4644, 4704, 4914, 5054, 5184, 5324, 5368

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

Cf. A050801.

Sequence in context: A223526 A032831 A047180 * A050801 A103093 A124632

Adjacent sequences: A051391 A051392 A051393 * A051395 A051396 A051397

Keyword

nonn

Author

Jud McCranie

Extensions

Sequence corrected and extended by Jonathan Sondow, Oct 28 2013

Corrected by Donovan Johnson, Oct 29 2013

Status

approved