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A070238
Sign of core(n)-phi(n) where core(n) is the squarefree part of n and phi the Euler totient function.
1
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
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
KEYWORD
easy,sign
AUTHOR
Benoit Cloitre, May 08 2002
EXTENSIONS
Comment section edited by Antti Karttunen, Nov 18 2017
STATUS
approved