A237282 - OEIS

%I #15 Sep 21 2016 09:08:40

%S 1,2,9,16,36,128,200,243,288,289,450,972,1024,1156,1600,2304,3600,

%T 6561,7776,8192,8214,8664,9126,9248,10584,12150,12800,14450,15987,

%U 18432,20808,24843,25000,26244,27075,28800,30250,33075,51005,56250,62208,63001,63948

%N The sum of the totatives of n is a perfect cube.

%C A positive integer <= n that is relatively prime to n is called a totative of n.

%H Charles R Greathouse IV, <a href="/A237282/b237282.txt">Table of n, a(n) for n = 1..2000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Totative.html">Totative</a>

%e 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 g[n_] := Module[{r, i},

%t     r = {};

%t     For[i = 1, i <= n, i++,

%t       If[GCD[n, i] == 1,

%t         r = Append[r, i]]];

%t     Apply[Plus, r]];

%t Select[Range[2*10^3], IntegerQ[g[#]^(1/3)] &]

%o (PARI) is(n)=ispower(n*eulerphi(n)/2, 3) || n==1 \\ _Charles R Greathouse IV_, Sep 21 2016

%Y Cf. A023896.

%K nonn

%O 1,2

%A _Joseph L. Pe_, Feb 05 2014

%E More terms from _Alois P. Heinz_, Feb 05 2014