A144857 Numbers k that divide Sum_{i=1..k} phi(i)^2, where phi(i) = totient function A000010.

1, 2, 3, 6, 26, 190, 610, 2078, 2670, 7038, 16466, 89973, 150374, 157298, 163367, 419090, 640627, 879702, 3479689, 5618437, 11304721, 74106171, 471591726, 475915439, 1198344149, 2270643086, 3051266010

Offset: 1

Author

Ctibor O. Zizka, Sep 23 2008

Keywords

• nonn
• more

Comments

Does a number k exist such that RootMeanSquare(phi(1), ..., phi(k)) is an integer?

Crossrefs

Cf. A000010, A057434, A048290, A140480.

Programs

Mathematica

lst = {}; s = 0; Do[ s = s + EulerPhi[n]^2; If[ Mod[s, n] == 0, AppendTo[lst, n]], {n, 10^9}]; lst (* Robert G. Wilson v, Oct 02 2008 *)

PARI

s=0;for(n=1,1e6,s+=eulerphi(n)^2;if(s%n==0,print1(n", "))) \\ Charles R Greathouse IV, Mar 05 2013

Formula

{k: k | A057434(k)}. - R. J. Mathar, Sep 29 2008

Extensions

a(8)-a(11) from R. J. Mathar, Sep 29 2008

a(12)-a(24) from Robert G. Wilson v, Oct 02 2008

a(25)-a(27) from Donovan Johnson, Aug 21 2011