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A346246 Dirichlet inverse of A344587, 2*A003961(n) - sigma(A003961(n)).

%I A346246 #18 Jul 20 2021 03:02:16
%S A346246 1,-2,-4,-1,-6,10,-10,-2,-3,14,-12,4,-16,22,26,-4,-18,2,-22,6,42,26,
%T A346246 -28,6,-5,34,-6,10,-30,-66,-36,-8,50,38,62,7,-40,46,66,10,-42,-106,
%U A346246 -46,12,14,58,-52,8,-9,2,74,16,-58,-2,74,18,90,62,-60,-18,-66,74,26,-16,98,-126,-70,18,114,-150,-72,18,-78,82,12,22
%N A346246 Dirichlet inverse of A344587, 2*A003961(n) - sigma(A003961(n)).
%C A346246 Dirichlet inverse of the deficiency of prime shifted n.
%H A346246 Antti Karttunen, <a href="/A346246/b346246.txt">Table of n, a(n) for n = 1..32768</a>
%H A346246 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A346246 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A346246 a(n) = A323910(A003961(n)).
%F A346246 a(n) = A346247(n) - A344587(n).
%o A346246 (PARI)
%o A346246 up_to = 16384;
%o A346246 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 A346246 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A346246 A344587(n) = { my(u=A003961(n)); (u+u - sigma(u)); };
%o A346246 v346246 = DirInverseCorrect(vector(up_to,n,A344587(n)));
%o A346246 A346246(n) = v346246[n];
%Y A346246 Cf. A000203, A003961, A003973, A323910, A344587, A346247, A346251 (positions of zeros).
%Y A346246 Cf. also A346235, A346248, A346254.
%K A346246 sign,look
%O A346246 1,2
%A A346246 _Antti Karttunen_, Jul 19 2021