A349396 - OEIS

%I #9 Nov 21 2021 01:18:14

%S 0,1,1,0,1,0,1,-1,-1,0,1,-2,1,0,0,-2,1,-6,1,-2,0,0,1,-2,-3,0,-3,-2,1,

%T 0,1,-3,0,0,0,2,1,0,0,-2,1,0,1,-2,-6,0,1,-2,-5,-20,0,-2,1,-6,0,-2,0,0,

%U 1,0,1,0,-6,-4,0,0,1,-2,0,0,1,8,1,0,-20,-2,0,0,1,-2,-5,0,1,0,0,0,0,-2,1,0,0,-2,0,0,0

%N Dirichlet convolution of A342001 ({arithmetic derivative of n}/A003557(n)) with A055615 (Dirichlet inverse of n).

%C Dirichlet convolution of this sequence with A000010 (Euler phi) is A346485.

%H Antti Karttunen, <a href="/A349396/b349396.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = Sum_{d|n} A055615(d) * A342001(n/d).

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A003557(n) = (n/factorback(factorint(n)[, 1]));

%o A342001(n) = (A003415(n) / A003557(n));

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

%o A349396(n) = sumdiv(n,d,A342001(n/d)*A055615(d));

%Y Cf. A003415, A003557, A055615, A342001.

%Y Cf. A346485, A347234,  A347235, A347395, A347954, A347959, A347961, A347963 for Dirichlet convolutions of A342001 with other sequences.

%Y Cf. also A349394.

%K sign

%O 1,12

%A _Antti Karttunen_, Nov 18 2021