%I #22 Jun 22 2017 06:58:01

%S 1,420,660,780,840,1320,1560,4620,5460,7140,7980,8580,9240,9660,10920,

%T 11220,12012,12180,12540,13020,13260,14280,14820,15180,15540,15708,

%U 15960,17160,17220,17556,17940,18060,18564,19140,19320,19380,19740

%N Numbers n such that the sign of core(n)-phi(n) is not equal to 2*mu(n)^2-1, where core(x) is the squarefree part of x.

%C Terms > 1 seem to be multiples of 3. For almost all k, sign(core(k)-phi(k)) = 2*mu(k)^2-1 = 2*A008683(k)^2-1.

%H Frank M Jackson, <a href="/A070237/b070237.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = C*n + O(n), with C a constant conjectured to be a(2) = 420.

%t core[n_] := Module[{m, fac=Select[FactorInteger[n], OddQ[#[[2]]] &]}, If[! SquareFreeQ[n],Times@@Table[fac[[m]][[1]], {m, Length[fac]}], n]]; checkQ[n_] := Module[{a=Abs[Sign[core[n]-EulerPhi[n]]-2*MoebiusMu[n]^2+1]}, If[a>0, True, False]]; Select[Range[25000], checkQ] (* _Frank M Jackson_, Jun 22 2017 *)

%o (PARI) for(n=1,25000,if(abs(sign(core(n)-eulerphi(n))-2*moebius(n)^2+1)>0,print1(n,",")))

%Y Cf. See A013929 for another interpretation.

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, May 08 2002

%E Comment and Pari code corrected by _Chris Boyd_, Mar 08 2014