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Dirichlet inverse of A344587, 2*A003961(n) - sigma(A003961(n)).
9

%I #18 Jul 20 2021 03:02:16

%S 1,-2,-4,-1,-6,10,-10,-2,-3,14,-12,4,-16,22,26,-4,-18,2,-22,6,42,26,

%T -28,6,-5,34,-6,10,-30,-66,-36,-8,50,38,62,7,-40,46,66,10,-42,-106,

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

%C Dirichlet inverse of the deficiency of prime shifted n.

%H Antti Karttunen, <a href="/A346246/b346246.txt">Table of n, a(n) for n = 1..32768</a>

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

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A323910(A003961(n)).

%F a(n) = A346247(n) - A344587(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 A344587(n) = { my(u=A003961(n)); (u+u - sigma(u)); };

%o v346246 = DirInverseCorrect(vector(up_to,n,A344587(n)));

%o A346246(n) = v346246[n];

%Y Cf. A000203, A003961, A003973, A323910, A344587, A346247, A346251 (positions of zeros).

%Y Cf. also A346235, A346248, A346254.

%K sign,look

%O 1,2

%A _Antti Karttunen_, Jul 19 2021