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

1,2

Comments

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..2000

Eric Weisstein's World of Mathematics, Totative

Example

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

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)] &]

Prog

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

Crossrefs

Cf. A023896.

Sequence in context: A275395 A213389 A304907 * A178440 A097965 A304974

Adjacent sequences: A237279 A237280 A237281 * A237283 A237284 A237285

Keyword

nonn

Author

Joseph L. Pe, Feb 05 2014

Extensions

More terms from Alois P. Heinz, Feb 05 2014

Status

approved