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%I #14 Sep 08 2022 08:46:05
%S 2,33,244,275,1025,1267,3126,3157,3368,4149,7777,10901,16808,16839,
%T 17050,17831,19932,24583,32769,33011,35893,49575,59050,59081,60073,
%U 62174,75856,91817,100001,100243,116807,159049,161052,161083,161294,162075,164176,168827
%N Numbers that are sums of two coprime positive fifth powers.
%e 244 is in the sequence since 1^5 + 3^5 = 244 and (1, 3) = 1.
%o (Magma) lst:=[]; for m in [2..168827] do f:=func<k | exists(q){x: x in [1..Floor((m-1)^(1/5))] | IsPower(k-x^5, 5)} and exists(r){x: x in [Floor((m-1)^(1/5))..1 by -1] | IsPower(k-x^5, 5)} select [q, r] else [-1, -1]>; if f(m)[1] gt 0 and GCD(f(m)[1], f(m)[2]) eq 1 then Append(~lst, m); end if; end for; lst; // _Arkadiusz Wesolowski_, Dec 19 2020
%Y Supersequence of A228556. Cf. A002561, A055014.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Aug 25 2013
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