cp's OEIS Frontend

A346254 Dirichlet inverse of A336849.

%I A346254 #13 Jul 20 2021 03:01:37
%S A346254 1,-3,-5,0,-7,25,-11,0,0,21,-13,-30,-17,55,35,0,-19,-100,-23,0,55,39,
%T A346254 -29,36,0,85,0,-66,-31,-175,-37,0,65,57,77,400,-41,115,85,0,-43,-495,
%U A346254 -47,108,0,145,-53,-216,0,98,171,-68,-59,500,169,0,115,93,-61,210,-67,111,0,0,119,-325,-71,0,261,-385,-73,-120,-79,205,0,-138
%N A346254 Dirichlet inverse of A336849.
%H A346254 Antti Karttunen, <a href="/A346254/b346254.txt">Table of n, a(n) for n = 1..16384</a>
%H A346254 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A346254 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A346254 a(n) = A346255(n) - A336849(n).
%o A346254 (PARI)
%o A346254 up_to = 16384;
%o A346254 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 A346254 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A346254 A336849(n) = { my(u=A003961(n)); (u/gcd(u, sigma(u))); };
%o A346254 v346254 = DirInverseCorrect(vector(up_to,n,A336849(n)));
%o A346254 A346254(n) = v346254[n];
%Y A346254 Cf. A000203, A003961, A003973, A336849, A346255, A346256 (positions of zeros).
%Y A346254 Cf. also A346235, A346246, A346248.
%K A346254 sign
%O A346254 1,2
%A A346254 _Antti Karttunen_, Jul 19 2021