A070237 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.

1, 420, 660, 780, 840, 1320, 1560, 4620, 5460, 7140, 7980, 8580, 9240, 9660, 10920, 11220, 12012, 12180, 12540, 13020, 13260, 14280, 14820, 15180, 15540, 15708, 15960, 17160, 17220, 17556, 17940, 18060, 18564, 19140, 19320, 19380, 19740

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

Cf. See A013929 for another interpretation.

Sequence in context: A200521 A350374 A189982 * A305416 A156687 A191934

Adjacent sequences: A070234 A070235 A070236 * A070238 A070239 A070240

Keyword

easy,nonn

Author

Benoit Cloitre, May 08 2002

Extensions

Comment and Pari code corrected by Chris Boyd, Mar 08 2014

Status

approved