A340146 - OEIS

%I #6 Dec 30 2020 20:00:15

%S 1,0,0,1,0,1,0,2,2,3,0,1,0,5,1,4,0,2,0,3,2,9,0,2,4,11,6,-3,0,2,0,8,4,

%T 15,5,4,0,17,5,6,0,3,0,9,-1,21,0,4,6,12,7,-5,0,6,9,18,8,27,0,3,0,29,4,

%U 16,2,-11,0,15,10,-6,0,8,0,35,4,-7,14,6,0,12,18,39,0,13,3,41,13,18,0,13,1,21,14,45,17,8

%N Möbius transform of A247074(x) = phi(x)/(Product_{primes p dividing x} gcd(p-1, x-1)).

%H Antti Karttunen, <a href="/A340146/b340146.txt">Table of n, a(n) for n = 1..8191</a>

%H Antti Karttunen, <a href="/A340146/a340146.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(n) = Sum_{d|n} A008683(n/d) * A247074(d).

%o (PARI)

%o A247074(n) = { my(f=factor(n)); eulerphi(f)/prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); }; \\ From A247074

%o A340146(n) = sumdiv(n,d,moebius(n/d)*A247074(d));

%Y Cf. A008683, A247074.

%Y Cf. also A340143, A340144, A340145.

%K sign

%O 1,8

%A _Antti Karttunen_, Dec 29 2020