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Integers that are not perfect fifth powers.
1

%I #16 Jul 03 2024 08:36:55

%S 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,

%T 27,28,29,30,31,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,

%U 51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70

%N Integers that are not perfect fifth powers.

%C Complement of A000584.

%H A. J. dos Reis and D. M. Silberger, <a href="https://doi.org/10.2307/2691513">Generating nonpowers by formula</a>, Math. Mag., 63 (1990), 53-55.

%t Complement[Range[#^5], Range[#]^5] & [3] (* _Paolo Xausa_, Jul 03 2024 *)

%o (Python)

%o from sympy import integer_nthroot

%o def A373868(n): return n+(k:=integer_nthroot(n, 5)[0])+(n>=(k+1)**5-k)

%Y Cf. A000037, A000583, A000584, A007412, A140823.

%K nonn,easy

%O 1,1

%A _Chai Wah Wu_, Jun 19 2024