cp's OEIS Frontend

A340191 Difference between A063994 and its Möbius transform.

%I A340191 #7 Dec 31 2020 15:35:25
%S A340191 0,1,1,1,1,2,1,1,2,4,1,1,1,6,5,1,1,1,1,1,7,10,1,1,4,12,2,1,1,0,1,1,11,
%T A340191 16,9,1,1,18,13,1,1,-2,1,1,4,22,1,1,6,1,17,1,1,1,13,3,19,28,1,1,1,30,
%U A340191 4,1,15,-6,1,1,23,-4,1,1,1,36,4,1,15,-8,1,1,2,40,1,3,19,42,29,1,1,5,17,1,31,46,21
%N A340191 Difference between A063994 and its Möbius transform.
%H A340191 Antti Karttunen, <a href="/A340191/b340191.txt">Table of n, a(n) for n = 1..8191</a>
%H A340191 Antti Karttunen, <a href="/A340191/a340191.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A340191 a(n) = A063994(n) - A340190(n).
%F A340191 a(n) = -Sum_{d|n, d<n} A008683(n/d) * A063994(d).
%o A340191 (PARI)
%o A340191 A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };
%o A340191 A340191(n) = -sumdiv(n,d,(d<n)*moebius(n/d)*A063994(d));
%Y A340191 Cf. A008683, A063994, A340190.
%K A340191 sign
%O A340191 1,6
%A A340191 _Antti Karttunen_, Dec 31 2020