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Dirichlet inverse of A341530, gcd(n*sigma(A003961(n)), sigma(n)*A003961(n)).
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%I #10 Jul 20 2021 03:01:46

%S 1,-1,-2,0,-2,-32,-4,-4,3,2,-2,34,-2,-16,-112,8,-2,125,-4,0,8,0,-6,

%T -128,3,-14,-8,-124,-2,8,-2,-10,-4,2,-320,920,-2,-4,4,8,-2,64,-4,-358,

%U 430,-12,-6,528,-3,-5,-352,16,-6,-368,-48,224,0,2,-2,104,-2,-12,-12,28,-4,16,-4,0,-36,400,-2,-440,-2,-2,450,8,-248,128

%N Dirichlet inverse of A341530, gcd(n*sigma(A003961(n)), sigma(n)*A003961(n)).

%H Antti Karttunen, <a href="/A346235/b346235.txt">Table of n, a(n) for n = 1..10000</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>

%o (PARI)

%o up_to = 65537;

%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 A341530(n) = { my(t=A003961(n), s=sigma(t)); gcd((n*s), sigma(n)*t); };

%o v346235 = DirInverseCorrect(vector(up_to,n,A341530(n)));

%o A346235(n) = v346235[n];

%Y Cf. A000203, A003961, A341530, A346236.

%Y Cf. also A346246, A346248, A346254.

%K sign

%O 1,3

%A _Antti Karttunen_, Jul 11 2021