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a(n) is the least integer such that floor(a(n)^(1/2)-a(n)^(1/3)) = n.
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%I #7 Mar 29 2015 14:06:18

%S 0,10,24,42,64,90,120,153,189,229,272,318,368,420,476,535,597,662,729,

%T 800,874,951,1031,1114,1199,1288,1379,1473,1570,1670,1773,1879,1987,

%U 2098,2212,2329,2449,2571,2696,2824,2954,3087,3223,3362,3504,3648,3795

%N a(n) is the least integer such that floor(a(n)^(1/2)-a(n)^(1/3)) = n.

%e 0^(1/2) - 0^(1/3) = 0.

%e 10^(1/2) - 10^(1/3) = 1.00784...

%e 24^(1/2) - 24^(1/3) = 2.01448...

%e 42^(1/2) - 42^(1/3) = 3.00471...

%t f[n_] := Block[{k = 0}, While[ Floor[k^(1/2) - k^(1/3)] < n, k++ ]; k]; Table[ f[n], {n, 0, 46}] (* _Robert G. Wilson v_, Mar 23 2005 *)

%K nonn

%O 0,2

%A _Ray G. Opao_, Mar 22 2005

%E a(27) and further terms from _Robert G. Wilson v_, Mar 23 2005