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A324641 Sum of the Doudna sequence and its Dirichlet inverse: a(n) = A005940(n) + A324640(n).

%I A324641 #5 Mar 11 2019 20:47:28
%S A324641 2,0,0,4,0,12,0,8,9,20,0,12,0,36,30,16,0,10,0,20,54,60,0,24,25,100,15,
%T A324641 36,0,48,0,32,90,44,90,28,0,84,150,40,0,32,0,60,97,180,0,48,81,146,66,
%U A324641 100,0,270,150,72,126,500,0,108,0,324,93,64,250,-128,0,44,270,-48,0,56,0,220,339,84,270,-48,0,80,391,308,0,140,110
%N A324641 Sum of the Doudna sequence and its Dirichlet inverse: a(n) = A005940(n) + A324640(n).
%H A324641 Antti Karttunen, <a href="/A324641/b324641.txt">Table of n, a(n) for n = 1..16384</a>
%F A324641 a(n) = A005940(n) + A324640(n).
%o A324641 (PARI)
%o A324641 up_to = 16384;
%o A324641 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 A324641 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
%o A324641 v324640 = DirInverse(vector(up_to,n,A005940(n)));
%o A324641 A324640(n) = v324640[n];
%o A324641 A324641(n) = (A005940(n)+A324640(n));
%K A324641 sign
%O A324641 1,1
%A A324641 _Antti Karttunen_, Mar 11 2019