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Dirichlet inverse of -A252748, 2*n - A003961(n).
9

%I #14 Jul 20 2021 10:45:56

%S 1,-1,-1,2,-3,5,-3,8,8,7,-9,10,-9,11,11,32,-15,16,-15,6,19,13,-17,48,

%T 8,17,56,18,-27,-3,-25,128,17,19,25,104,-33,23,25,32,-39,9,-39,-6,24,

%U 29,-41,224,32,16,23,6,-47,144,35,88,31,31,-57,78,-55,37,72,512,43,-33,-63,-18,41,-13,-69,512,-67,41,40,-6,43

%N Dirichlet inverse of -A252748, 2*n - A003961(n).

%C Zeros occur at n = 352, 26840, 34816, 3787168, ...

%H Antti Karttunen, <a href="/A346248/b346248.txt">Table of n, a(n) for n = 1..34816</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A346250(n) + A252748(n).

%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 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961

%o v346248 = DirInverseCorrect(vector(up_to,n,(n+n)-A003961(n)));

%o A346248(n) = v346248[n];

%Y Cf. A003961, A252748, A346250.

%Y Cf. also A323910, A346235, A346246, A346254.

%K sign,look

%O 1,4

%A _Antti Karttunen_, Jul 19 2021