cp's OEIS Frontend

A349571 Dirichlet convolution of A048673 with A055615 (Dirichlet inverse of n).

%I A349571 #14 Nov 26 2021 16:18:08
%S A349571 1,0,0,1,-1,2,-1,4,4,3,-4,4,-4,5,6,13,-7,6,-7,5,10,6,-8,10,5,8,24,9,
%T A349571 -13,-2,-12,40,12,9,16,16,-16,11,16,11,-19,-2,-19,8,14,14,-20,28,19,9,
%U A349571 18,12,-23,26,22,21,22,15,-28,2,-27,18,26,121,28,-8,-31,11,28,-8,-34,46,-33,20,18,15,34,-8,-37,29,124
%N A349571 Dirichlet convolution of A048673 with A055615 (Dirichlet inverse of n).
%C A349571 Also Dirichlet convolution of A349385 with A349387.
%H A349571 Antti Karttunen, <a href="/A349571/b349571.txt">Table of n, a(n) for n = 1..20000</a>
%H A349571 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A349571 a(n) = Sum_{d|n} A048673(n/d) * A055615(d).
%F A349571 a(n) = Sum_{d|n} A349385(n/d) * A349387(d).
%t A349571 f[p_, e_] := NextPrime[p]^e; s[1] = 1; s[n_] := (1 + Times @@ f @@@ FactorInteger[n])/2; a[n_] := DivisorSum[n, # * MoebiusMu[#] * s[n/#] &]; Array[a, 100] (* _Amiram Eldar_, Nov 23 2021 *)
%o A349571 (PARI)
%o A349571 A048673(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (1/2)*(1+factorback(f)); };
%o A349571 A055615(n) = (n*moebius(n));
%o A349571 A349571(n) = sumdiv(n,d,A048673(n/d)*A055615(d));
%Y A349571 Cf. A048673, A055615, A349385, A349387, A349572 (Dirichlet inverse).
%Y A349571 Cf. also A349398, A349573.
%K A349571 sign
%O A349571 1,6
%A A349571 _Antti Karttunen_, Nov 23 2021