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A378531 Dirichlet convolution of A378432 and A378542.

%I A378531 #8 Dec 01 2024 13:41:43
%S A378531 1,0,0,2,0,3,0,2,2,3,0,4,0,3,3,6,0,4,0,4,3,3,0,14,2,3,2,4,0,6,0,10,3,
%T A378531 3,3,18,0,3,3,14,0,6,0,4,4,3,0,30,2,4,3,4,0,14,3,14,3,3,0,30,0,3,4,22,
%U A378531 3,6,0,4,3,6,0,48,0,3,4,4,3,6,0,30,6,3,0,30,3,3,3,14,0,30,3,4,3,3,3,74,0,4,4,18
%N A378531 Dirichlet convolution of A378432 and A378542.
%C A378531 Möbius transform of A378533.
%H A378531 Antti Karttunen, <a href="/A378531/b378531.txt">Table of n, a(n) for n = 1..65537</a>
%F A378531 a(n) = Sum_{d|n} A378432(d)*A378542(n/d).
%F A378531 a(n) = Sum_{d|n} A008683(d)*A378533(n/d).
%o A378531 (PARI)
%o A378531 A033879(n) = ((2*n)-sigma(n));
%o A378531 A296075(n) = sumdiv(n,d,A033879(d));
%o A378531 memoA378432 = Map();
%o A378531 A378432(n) = if(1==n,1,my(v); if(mapisdefined(memoA378432,n,&v), v, v = -sumdiv(n,d,if(d<n,A296075(n/d)*A378432(d),0)); mapput(memoA378432,n,v); (v)));
%o A378531 A378542(n) = sumdiv(n,d,d*!(bigomega(n/d)%2));
%o A378531 A378531(n) = sumdiv(n,d,A378432(d)*A378542(n/d));
%Y A378531 Cf. A008683, A378532 (Dirichlet inverse), A378432, A378533 (inverse Möbius transform), A378542.
%Y A378531 Cf. also A345182.
%K A378531 nonn
%O A378531 1,4
%A A378531 _Antti Karttunen_, Dec 01 2024