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A237282 The sum of the totatives of n is a perfect cube.

%I A237282 #16 Feb 16 2025 08:33:21
%S A237282 1,2,9,16,36,128,200,243,288,289,450,972,1024,1156,1600,2304,3600,
%T A237282 6561,7776,8192,8214,8664,9126,9248,10584,12150,12800,14450,15987,
%U A237282 18432,20808,24843,25000,26244,27075,28800,30250,33075,51005,56250,62208,63001,63948
%N A237282 The sum of the totatives of n is a perfect cube.
%C A237282 A positive integer <= n that is relatively prime to n is called a totative of n.
%H A237282 Charles R Greathouse IV, <a href="/A237282/b237282.txt">Table of n, a(n) for n = 1..2000</a>
%H A237282 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Totative.html">Totative</a>
%e A237282 The sum of totatives of 9 is 1 + 2 + 4 + 5 + 7 + 8 = 27 = 3^3; therefore, 9 is a term of the sequence.
%t A237282 g[n_] := Module[{r, i},
%t A237282     r = {};
%t A237282     For[i = 1, i <= n, i++,
%t A237282       If[GCD[n, i] == 1,
%t A237282         r = Append[r, i]]];
%t A237282     Apply[Plus, r]];
%t A237282 Select[Range[2*10^3], IntegerQ[g[#]^(1/3)] &]
%o A237282 (PARI) is(n)=ispower(n*eulerphi(n)/2, 3) || n==1 \\ _Charles R Greathouse IV_, Sep 21 2016
%Y A237282 Cf. A023896.
%K A237282 nonn
%O A237282 1,2
%A A237282 _Joseph L. Pe_, Feb 05 2014
%E A237282 More terms from _Alois P. Heinz_, Feb 05 2014