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A340048 Numbers that are the sum of a cube s and a fourth power t such that 0 < s <= t.

%I A340048 #19 Feb 17 2021 11:47:18
%S A340048 2,17,24,82,89,108,145,257,264,283,320,381,472,626,633,652,689,750,
%T A340048 841,968,1137,1297,1304,1323,1360,1421,1512,1639,1808,2025,2296,2402,
%U A340048 2409,2428,2465,2526,2617,2744,2913,3130,3401,3732,4097,4104,4123,4129,4160,4221,4312
%N A340048 Numbers that are the sum of a cube s and a fourth power t such that 0 < s <= t.
%C A340048 Contains the entries of A340050 and numbers like 2, 8192, 1062882,.. which are 2 times 12th powers (A008456). - _R. J. Mathar_, Jan 05 2021
%e A340048 24 is in the sequence since 2^3 + 2^4 = 8 + 16 = 24, where 0 < 8 <= 16.
%p A340048 isA340048 := proc(n)
%p A340048     local t,s3 ;
%p A340048     for t from 0 do
%p A340048         s3 := n-t^4 ;
%p A340048         if s3 <= 0 then
%p A340048             return false ;
%p A340048         elif s3 <= t^4 and isA000578(s3) then
%p A340048             return true;
%p A340048         end if;
%p A340048     end do:
%p A340048 end proc:
%p A340048 for n from 1 do
%p A340048     if isA340048(n) then
%p A340048         printf("%d,\n",n) ;
%p A340048     end if;
%p A340048 end do: # _R. J. Mathar_, Jan 05 2021
%t A340048 Table[If[Sum[(Floor[i^(1/3)] - Floor[(i - 1)^(1/3)]) (Floor[(n - i)^(1/4)] - Floor[(n - i - 1)^(1/4)]), {i, Floor[n/2]}] > 0, n, {}], {n, 1000}] // Flatten
%o A340048 (Python)
%o A340048 def aupto(lim):
%o A340048   cubes = [i**3 for i in range(1, int(lim**(1/3))+2)]
%o A340048   fours = [i**4 for i in range(1, int(lim**(1/4))+2)]
%o A340048   return sorted(s+t for s in cubes for t in fours if t >= s and s+t <= lim)
%o A340048 print(aupto(4312)) # _Michael S. Branicky_, Feb 17 2021
%Y A340048 Cf. A010057.
%Y A340048 Cf. A008456, A340050.
%K A340048 nonn
%O A340048 1,1
%A A340048 _Wesley Ivan Hurt_, Dec 26 2020