A070238 Sign of core(n)-phi(n) where core(n) is the squarefree part of n and phi the Euler totient function.

0, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1

Offset

1,1

Comments

Sum_{k=1..n} a(k) > 0 for n > 1. That is, the partial sums stay positive forever.

For almost all n, a(n) = 2*mu(n)^2 - 1 = 2*A008966(n) - 1. Below 1000, there are only 5 exceptions: n=1, 420, 660, 780, 840. The exceptions are given by A070237.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = sign(A007913(n) - A000010(n)).

Mathematica

Array[Sign[Sqrt[#] /. (c_: 1) a_^(b_: 0) :> (c a^b)^2 - EulerPhi@ #] &, 100] (* Michael De Vlieger, Nov 18 2017, after Bill Gosper at A007913 *)

Prog

(PARI) for(n=1, 100, print1(sign(core(n)-eulerphi(n)), ", "))

Crossrefs

Cf. A000010, A007913, A008683, A008966, A070237.

Sequence in context: A165476 A165596 A226523 * A062157 A103131 A112347

Adjacent sequences: A070235 A070236 A070237 * A070239 A070240 A070241

Keyword

easy,sign

Author

Benoit Cloitre, May 08 2002

Extensions

Comment section edited by Antti Karttunen, Nov 18 2017

Status

approved