cp's OEIS Frontend

A354821 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d A342001(n/d) * a(d).

%I A354821 #8 Jun 09 2022 08:45:00
%S A354821 1,-1,-1,-1,-1,-3,-1,0,-1,-5,-1,3,-1,-7,-6,1,-1,4,-1,3,-8,-11,-1,8,-1,
%T A354821 -13,0,3,-1,3,-1,1,-12,-17,-10,17,-1,-19,-14,12,-1,1,-1,3,4,-23,-1,3,
%U A354821 -1,6,-18,3,-1,8,-14,16,-20,-29,-1,62,-1,-31,4,0,-16,-3,-1,3,-24,-9,-1,-6,-1,-37,6,3,-16,-5,-1,7,1
%N A354821 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A342001(n/d) * a(d).
%C A354821 Dirichlet inverse of pointwise sum of A342001 (arithmetic derivative of n / A003557(n)) and A063524 (1, 0, 0, 0, ...).
%H A354821 Antti Karttunen, <a href="/A354821/b354821.txt">Table of n, a(n) for n = 1..10080</a>
%H A354821 Antti Karttunen, <a href="/A354821/a354821.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%o A354821 (PARI)
%o A354821 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A354821 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A354821 A342001(n) = (A003415(n) / A003557(n));
%o A354821 memoA354821 = Map();
%o A354821 A354821(n) = if(1==n,1,my(v); if(mapisdefined(memoA354821,n,&v), v, v = -sumdiv(n,d,if(d<n,A342001(n/d)*A354821(d),0)); mapput(memoA354821,n,v); (v)));
%Y A354821 Cf. A003415, A003557, A063524, A342001.
%Y A354821 Cf. also A346241.
%K A354821 sign
%O A354821 1,6
%A A354821 _Antti Karttunen_, Jun 08 2022