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

1, 2, 9, 16, 36, 128, 200, 243, 288, 289, 450, 972, 1024, 1156, 1600, 2304, 3600, 6561, 7776, 8192, 8214, 8664, 9126, 9248, 10584, 12150, 12800, 14450, 15987, 18432, 20808, 24843, 25000, 26244, 27075, 28800, 30250, 33075, 51005, 56250, 62208, 63001, 63948

Offset: 1

Author

Joseph L. Pe, Feb 05 2014

Keywords

• nonn

Comments

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

Examples

			The sum of totatives of 9 is 1 + 2 + 4 + 5 + 7 + 8 = 27 = 3^3; therefore, 9 is a term of the sequence.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..2000
• Eric Weisstein's World of Mathematics, Totative

Crossrefs

Cf. A023896.

Programs

Mathematica

g[n_] := Module[{r, i},
    r = {};
    For[i = 1, i <= n, i++,
      If[GCD[n, i] == 1,
        r = Append[r, i]]];
    Apply[Plus, r]];
Select[Range[2*10^3], IntegerQ[g[#]^(1/3)] &]

PARI

is(n)=ispower(n*eulerphi(n)/2, 3) || n==1 \\ Charles R Greathouse IV, Sep 21 2016

Extensions

More terms from Alois P. Heinz, Feb 05 2014