cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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