A369455 - OEIS

%I #8 Jan 27 2024 16:05:56

%S 0,1,1,-1,1,0,1,1,-1,0,1,-3,1,0,0,-4,1,-6,1,-3,0,0,1,0,-3,0,-5,-3,1,0,

%T 1,1,0,0,0,9,1,0,0,0,1,0,1,-3,-6,0,1,-3,-5,-20,0,-3,1,-8,0,0,0,0,1,0,

%U 1,0,-6,-7,0,0,1,-3,0,0,1,-6,1,0,-20,-3,0,0,1,-3,1,0,1,0,0,0,0,0,1,0,0,-3,0,0,0,0,1,-42,-6,29

%N Dirichlet convolution of A083345 with A055615 (Dirichlet inverse of n), where A083345(n) = (n'/gcd(n,n')) and n' is the arithmetic derivative of n.

%C Dirichlet convolution of this sequence with A000010 (Euler phi) is A369068.

%H Antti Karttunen, <a href="/A369455/b369455.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = Sum_{d|n} A055615(n/d)*A083345(d).

%o (PARI)

%o A055615(n) = (n*moebius(n));

%o A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };

%o A369455(n) = sumdiv(n, d, A083345(n/d)*A055615(d));

%Y Cf. A055615, A083345.

%Y Cf. also A349394, A349396, A369068, A369069.

%K sign

%O 1,12

%A _Antti Karttunen_, Jan 27 2024