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Numbers not the sum of at most three perfect powers (A001597).
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%I #12 May 07 2017 11:24:57

%S 7,15,23,87,111,119,167,335,1391,1455,1607,1679,1991,25887,26375

%N Numbers not the sum of at most three perfect powers (A001597).

%C Cannot be written in the form a^x + b^y + c^z with a, b, c >= 0 and x, y, z > 1.

%C a(16), if it exists, is larger than 10^8. - _Giovanni Resta_, May 07 2017

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectPower.html">Perfect Power</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerfulNumber.html">Powerful Number.</a>

%t 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 A056828 is a subset, A001694, A274459.

%K nonn,more

%O 1,1

%A R. P. van der Hilst (R.P.vanderHilst(AT)students.uu.nl), Jan 12 2006

%E Edited by _Robert G. Wilson v_, May 01 2006