cp's OEIS Frontend

A346236 Sum of A341530 and its Dirichlet inverse.

%I A346236 #9 Jul 20 2021 03:01:57
%S A346236 2,0,0,1,0,4,0,1,4,4,0,70,0,8,8,9,0,134,0,2,16,4,0,52,4,4,-4,44,0,368,
%T A346236 0,-3,8,4,16,1037,0,8,8,18,0,352,0,6,460,12,0,564,16,-2,8,34,0,-296,8,
%U A346236 344,16,4,0,464,0,4,-8,29,8,160,0,2,24,736,0,-395,0,4,460,20,16,200,0,-14,21,4,0,2152,8,8,8,740
%N A346236 Sum of A341530 and its Dirichlet inverse.
%H A346236 Antti Karttunen, <a href="/A346236/b346236.txt">Table of n, a(n) for n = 1..16384</a>
%H A346236 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A346236 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A346236 a(n) = A341530(n) + A346235(n).
%o A346236 (PARI)
%o A346236 up_to = 65537;
%o A346236 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 A346236 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A346236 A341530(n) = { my(t=A003961(n), s=sigma(t)); gcd((n*s), sigma(n)*t); };
%o A346236 v346235 = DirInverseCorrect(vector(up_to,n,A341530(n)));
%o A346236 A346235(n) = v346235[n];
%o A346236 A346236(n) = (A341530(n)+A346235(n));
%Y A346236 Cf. A000203, A003961, A341530, A346235.
%Y A346236 Cf. also A346247, A346250, A346255.
%K A346236 sign
%O A346236 1,1
%A A346236 _Antti Karttunen_, Jul 11 2021