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A354828 Denominators of Dirichlet inverse of fraction A003961(n) / sigma(n).

%I A354828 #8 Jun 07 2022 16:23:27
%S A354828 1,1,4,7,6,4,8,35,208,6,12,14,14,8,24,7595,18,208,20,3,32,12,24,7,
%T A354828 1116,14,832,28,30,24,32,7595,48,18,48,728,38,20,56,15,42,32,44,42,
%U A354828 416,24,48,1519,3648,1116,72,49,54,832,72,35,16,30,60,12,62,32,1664,33759775,12,48,68,63,96,48,72,182,74,38,4464
%N A354828 Denominators of Dirichlet inverse of fraction A003961(n) / sigma(n).
%H A354828 Antti Karttunen, <a href="/A354828/b354828.txt">Table of n, a(n) for n = 1..65537</a>
%H A354828 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A354828 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A354828 (PARI)
%o A354828 up_to = 65537;
%o A354828 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A354828 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 A354828 AuxA354827(n) = (A003961(n)/sigma(n));
%o A354828 vDirInv = DirInverseCorrect(vector(up_to,n,AuxA354827(n)));
%o A354828 A354828(n) = denominator(vDirInv[n]);
%Y A354828 Cf. A000203, A003961, A349161, A349162.
%Y A354828 Cf. A354827 (denominators).
%Y A354828 Cf. also A349628, A354366.
%K A354828 nonn,frac
%O A354828 1,3
%A A354828 _Antti Karttunen_, Jun 07 2022