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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A024410 A200521 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

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Last modified May 16 21:28 EDT 2021. Contains 343951 sequences. (Running on oeis4.)