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A371587 a(n) is the number of integers m from 1 to n inclusive such that m^m is a cube.

%I A371587 #25 Aug 12 2025 11:24:16
%S A371587 1,1,2,2,2,3,3,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,
%T A371587 12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,19,19,19,
%U A371587 20,20,20,21,21,21,22,22,22,23,24,24,25,25,25,26,26,26,27,27,27,28,28
%N A371587 a(n) is the number of integers m from 1 to n inclusive such that m^m is a cube.
%C A371587 Dick Hess gave a puzzle at a "Gathering for Gardner" meeting asking for a(40).
%C A371587 a(n) is the number of integers not exceeding n that are divisible by 3 plus the number of cubes in the same range that are not divisible by 3.
%H A371587 Harvey P. Dale, <a href="/A371587/b371587.txt">Table of n, a(n) for n = 1..1000</a>
%F A371587 a(n) = floor(n/3) + floor(n^(1/3)) - floor(n^(1/3)/3).
%e A371587 Suppose n = 40. There are 13 numbers in the range that are divisible by 3 and should be counted. In addition, there are two cubes 1 and 8 that are not divisible by 3. Thus, a(40) = 15.
%t A371587 Table[Floor[n/3] + Floor[n^(1/3)] - Floor[n^(1/3)/3], {n, 100}]
%t A371587 Accumulate[Table[If[IntegerQ[CubeRoot[n^n]],1,0],{n,100}]] (* _Harvey P. Dale_, Aug 12 2025 *)
%o A371587 (Python)
%o A371587 from sympy import integer_nthroot
%o A371587 def A371587(n): return n//3+integer_nthroot(n,3)[0]-integer_nthroot(n//27,3)[0] # _Chai Wah Wu_, Sep 18 2024
%Y A371587 Cf. A000578, A329547.
%K A371587 nonn
%O A371587 1,3
%A A371587 _Tanya Khovanova_, Mar 28 2024