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a(n) is the number of integers m from 1 to n inclusive such that m^m is a cube.
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%I #20 Sep 18 2024 16:33:23

%S 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 12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,19,19,19,

%U 20,20,20,21,21,21,22,22,22,23,24,24,25,25,25,26,26,26,27,27,27,28,28

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

%C Dick Hess gave a puzzle at a "Gathering for Gardner" meeting asking for a(40).

%C 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.

%F a(n) = floor(n/3) + floor(n^(1/3)) - floor(n^(1/3)/3).

%e 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 Table[Floor[n/3] + Floor[n^(1/3)] - Floor[n^(1/3)/3], {n, 100}]

%o (Python)

%o from sympy import integer_nthroot

%o def A371587(n): return n//3+integer_nthroot(n,3)[0]-integer_nthroot(n//27,3)[0] # _Chai Wah Wu_, Sep 18 2024

%Y Cf. A000578, A329547.

%K nonn

%O 1,3

%A _Tanya Khovanova_, Mar 28 2024