A323408 - OEIS

%I #9 Jan 15 2019 18:43:21

%S 2,0,0,1,0,4,0,5,4,8,0,10,0,12,16,15,0,12,0,20,24,20,0,18,16,24,24,30,

%T 0,0,0,35,40,32,48,32,0,36,48,36,0,0,0,50,48,44,0,30,36,32,64,60,0,28,

%U 80,54,72,56,0,8,0,60,72,71,96,0,0,80,88,0,0,64,0,72,64,90,120,0,0,60,88,80,0,12,128,84,112,90,0,16,144,110,120

%N Sum of unitary phi and its Dirichlet inverse: a(n) = A047994(n) + A323407(n).

%H Antti Karttunen, <a href="/A323408/b323408.txt">Table of n, a(n) for n = 1..16384</a>

%o (PARI)

%o up_to = 65537;

%o DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.

%o A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };

%o v323407 = DirInverse(vector(up_to,n,A047994(n)));

%o A323407(n) = v323407[n];

%o A323408(n) = (A047994(n) + A323407(n));

%Y Cf. A047994, A323407.

%Y Cf. also A319340, A322581, A323364, A323399, A323403.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jan 15 2019