A340190 - OEIS

%I #9 Dec 31 2020 15:35:06

%S 1,0,1,0,3,-1,5,0,0,-3,9,0,11,-5,-1,0,15,0,17,0,-3,-9,21,0,0,-11,0,2,

%T 27,1,29,0,-7,-15,-5,0,35,-17,-9,0,39,3,41,0,4,-21,45,0,0,0,-13,2,51,

%U 0,-9,-2,-15,-27,57,0,59,-29,0,0,1,11,65,0,-19,7,69,0,71,-35,0,2,-11,9,77,0,0,-39,81,-2,-3,-41,-25

%N Möbius transform of A063994(x) = Product_{primes p dividing x} gcd(p-1, x-1).

%H Antti Karttunen, <a href="/A340190/b340190.txt">Table of n, a(n) for n = 1..8191</a>

%H Antti Karttunen, <a href="/A340190/a340190.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(n) = Sum_{d|n} A008683(n/d) * A063994(d).

%F a(n) = A063994(n) - A340191(n).

%o (PARI)

%o A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };

%o A340190(n) = sumdiv(n,d,moebius(n/d)*A063994(d));

%Y Cf. A008683, A063994, A340191.

%Y Cf. also A007431, A340143, A340146, A340192.

%K sign

%O 1,5

%A _Antti Karttunen_, Dec 31 2020