This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A113505 #19 Jun 16 2025 00:36:20
%S A113505 7,15,23,87,111,119,167,335,1391,1455,1607,1679,1991,25887,26375
%N A113505 Numbers not the sum of at most three perfect powers (A001597).
%C A113505 Cannot be written in the form a^x + b^y + c^z with a, b, c >= 0 and x, y, z > 1.
%C A113505 a(16), if it exists, is larger than 10^8. - _Giovanni Resta_, May 07 2017
%C A113505 From _Brian Trial_, Jun 07 2025: (Start)
%C A113505 Per Legendre's three-square theorem (A004215) only integers of the form 4^i(8j+7) are eligible.
%C A113505 Every integer > 5042631 (= 1424^2 + 734*2 + 19^5) and < 10^9 can be expressed as either a^2 + b^2 + c^2 or a^2 + b^2 + c^3, a,b,c >= 0 so a(16) >= 10^9. (End)
%H A113505 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectPower.html">Perfect Power</a>
%H A113505 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerfulNumber.html">Powerful Number.</a>
%t A113505 lmt = 40000; s = Union@ Join[{0, 1}, Flatten@ Table[n^i, {n, 2, Sqrt@ lmt}, {i, 2, Log[n, lmt]}]]; t = Select[ Union[Plus @@@ Tuples[s, 3]], # < lmt + 1 &]; Complement[Range@ lmt, t] (* _Robert G. Wilson v_ *)
%Y A113505 A056828 is a subset, A001694, A274459.
%K A113505 nonn,more
%O A113505 1,1
%A A113505 R. P. van der Hilst (R.P.vanderHilst(AT)students.uu.nl), Jan 12 2006
%E A113505 Edited by _Robert G. Wilson v_, May 01 2006