cp's OEIS Frontend

A346255 Sum of A336849 and its Dirichlet inverse.

%I A346255 #10 Jul 20 2021 03:02:06
%S A346255 2,0,0,9,0,30,0,27,25,42,0,-15,0,66,70,81,0,-25,0,63,110,78,0,45,49,
%T A346255 102,125,-33,0,-140,0,243,130,114,154,625,0,138,170,189,0,-440,0,117,
%U A346255 175,174,0,-81,121,147,190,-51,0,625,182,99,230,186,0,315,0,222,275,729,238,-260,0,171,290,-308,0,15,0,246,245,-69,286
%N A346255 Sum of A336849 and its Dirichlet inverse.
%H A346255 Antti Karttunen, <a href="/A346255/b346255.txt">Table of n, a(n) for n = 1..16384</a>
%H A346255 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A346255 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A346255 a(n) = A336849(n) + A346254(n).
%o A346255 (PARI)
%o A346255 up_to = 16384;
%o A346255 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 A346255 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A346255 A336849(n) = { my(u=A003961(n)); (u/gcd(u, sigma(u))); };
%o A346255 v346254 = DirInverseCorrect(vector(up_to,n,A336849(n)));
%o A346255 A346254(n) = v346254[n];
%o A346255 A346255(n) = (A336849(n)+A346254(n));
%Y A346255 Cf. A000203, A003961, A003973, A336849, A346254.
%Y A346255 Cf. also A346236, A346247, A346250.
%K A346255 sign
%O A346255 1,1
%A A346255 _Antti Karttunen_, Jul 19 2021