|
%I #25 Nov 19 2017 03:51:50
%S 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,
%T 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,
%U 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
%N Sign of core(n)-phi(n) where core(n) is the squarefree part of n and phi the Euler totient function.
%C Sum_{k=1..n} a(k) > 0 for n > 1. That is, the partial sums stay positive forever.
%C 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.
%H Antti Karttunen, <a href="/A070238/b070238.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = sign(A007913(n) - A000010(n)).
%t 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 *)
%o (PARI) for(n=1,100,print1(sign(core(n)-eulerphi(n)),","))
%Y Cf. A000010, A007913, A008683, A008966, A070237.
%K easy,sign
%O 1,1
%A _Benoit Cloitre_, May 08 2002
%E Comment section edited by _Antti Karttunen_, Nov 18 2017
|
