OFFSET
1,2
COMMENTS
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.
LINKS
Frank M Jackson, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = C*n + O(n), with C a constant conjectured to be a(2) = 420.
MATHEMATICA
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 *)
PROG
(PARI) for(n=1, 25000, if(abs(sign(core(n)-eulerphi(n))-2*moebius(n)^2+1)>0, print1(n, ", ")))
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 08 2002
EXTENSIONS
Comment and Pari code corrected by Chris Boyd, Mar 08 2014
STATUS
approved