cp's OEIS Frontend

A340143 Möbius transform of A160595, where A160595(x) = phi(x)/gcd(phi(x), x-1).

%I A340143 #10 Dec 29 2020 20:38:23
%S A340143 1,0,0,1,0,1,0,2,2,3,0,1,0,5,3,4,0,2,0,3,2,9,0,2,4,11,6,-3,0,0,0,8,4,
%T A340143 15,11,4,0,17,11,6,0,3,0,9,0,21,0,4,6,12,15,-5,0,6,19,18,8,27,0,3,0,
%U A340143 29,13,16,2,-11,0,15,10,-12,0,8,0,35,12,-7,14,0,0,12,18,39,0,13,15,41,27,18,0,12,3,21,14,45,35
%N A340143 Möbius transform of A160595, where A160595(x) = phi(x)/gcd(phi(x), x-1).
%H A340143 Antti Karttunen, <a href="/A340143/b340143.txt">Table of n, a(n) for n = 1..8191</a>
%H A340143 Antti Karttunen, <a href="/A340143/a340143.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A340143 a(n) = Sum_{d|n} A008683(n/d) * A160595(d).
%t A340143 Table[DivisorSum[n, MoebiusMu[n/#1]*#2/GCD[#2, #3] & @@ {#, EulerPhi[#], # - 1} &], {n, 95}] (* _Michael De Vlieger_, Dec 29 2020 *)
%o A340143 (PARI)
%o A340143 A160595(n) = { my(x=eulerphi(n)); x/gcd(x,n-1); };
%o A340143 A340143(n) = sumdiv(n,d,moebius(n/d)*A160595(d));
%Y A340143 Cf. A008683, A160595.
%Y A340143 Cf. also A340141, A340142.
%K A340143 sign
%O A340143 1,8
%A A340143 _Antti Karttunen_, Dec 29 2020