A346480 - OEIS

%I #16 Nov 02 2021 10:29:36

%S 2,0,0,9,0,30,0,27,25,42,0,45,0,66,70,45,0,75,0,99,110,78,0,3,49,102,

%T 125,135,0,60,0,81,130,114,154,-39,0,138,170,15,0,60,0,261,175,174,0,

%U 117,121,231,190,297,0,-225,182,3,230,186,0,-381,0,222,275,189,238,360,0,423,290,216,0,381,0,246,245,459

%N Sum of A250469 and its Dirichlet inverse.

%H Antti Karttunen, <a href="/A346480/b346480.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%F a(n) = A250469(n) + A346479(n).

%F a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A250469(d) * A346479(n/d).

%o (PARI)

%o up_to = 16384;

%o DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*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 v346479 = DirInverseCorrect(vector(up_to,n,A250469(n)));

%o A346479(n) = v346479[n];

%o A346480(n) = (A250469(n)+A346479(n));

%o (PARI) A346480(n) = if(1==n, 2, -sumdiv(n,d,if((1==d)||n==d,0,A250469(d)*A346479(n/d)))); \\ (Demonstrates the convolution formula).

%Y Cf. A250469, A346479.

%Y Cf. also A346478.

%K sign

%O 1,1

%A _Antti Karttunen_, Jul 30 2021