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A378217 Dirichlet inverse of A330575.

%I A378217 #6 Nov 22 2024 20:32:53
%S A378217 1,-3,-4,1,-6,10,-8,1,2,16,-12,-2,-14,22,22,1,-18,-2,-20,-4,30,34,-24,
%T A378217 -2,4,40,2,-6,-30,-52,-32,1,46,52,46,-2,-38,58,54,-4,-42,-72,-44,-10,
%U A378217 -8,70,-48,-2,6,-4,70,-12,-54,-2,70,-6,78,88,-60,8,-62,94,-12,1,82,-112,-68,-16,94,-116,-72,-2,-74,112,-8,-18,94
%N A378217 Dirichlet inverse of A330575.
%H A378217 Antti Karttunen, <a href="/A378217/b378217.txt">Table of n, a(n) for n = 1..65537</a>
%F A378217 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A330575(n/d) * a(d).
%o A378217 (PARI)
%o A378217 memoA330575 = Map();
%o A378217 A330575(n) = if(1==n,1,my(v); if(mapisdefined(memoA330575,n,&v), v, v = n + sumdiv(n,d,if(d<n,A330575(d),0)); mapput(memoA330575,n,v); (v)));
%o A378217 memoA378217 = Map();
%o A378217 A378217(n) = if(1==n,1,my(v); if(mapisdefined(memoA378217,n,&v), v, v = -sumdiv(n,d,if(d<n,A330575(n/d)*A378217(d),0)); mapput(memoA378217,n,v); (v)));
%Y A378217 Cf. A330575.
%K A378217 sign
%O A378217 1,2
%A A378217 _Antti Karttunen_, Nov 22 2024