cp's OEIS Frontend

A378532 Dirichlet convolution of A296075 and A378525.

%I A378532 #8 Dec 01 2024 13:41:11
%S A378532 1,0,0,-2,0,-3,0,-2,-2,-3,0,-4,0,-3,-3,-2,0,-4,0,-4,-3,-3,0,-2,-2,-3,
%T A378532 -2,-4,0,-6,0,-2,-3,-3,-3,-1,0,-3,-3,-2,0,-6,0,-4,-4,-3,0,-2,-2,-4,-3,
%U A378532 -4,0,-2,-3,-2,-3,-3,0,0,0,-3,-4,-2,-3,-6,0,-4,-3,-6,0,0,0,-3,-4,-4,-3,-6,0,-2,-2,-3,0,0,-3,-3,-3,-2
%N A378532 Dirichlet convolution of A296075 and A378525.
%C A378532 Inverse Möbius transform of A378534.
%H A378532 Antti Karttunen, <a href="/A378532/b378532.txt">Table of n, a(n) for n = 1..65537</a>
%F A378532 a(n) = Sum_{d|n} A296075(d)*A378525(n/d).
%F A378532 a(n) = Sum_{d|n} A378534(d).
%o A378532 (PARI)
%o A378532 A033879(n) = ((2*n)-sigma(n));
%o A378532 A296075(n) = sumdiv(n,d,A033879(d));
%o A378532 A378542(n) = sumdiv(n,d,d*!(bigomega(n/d)%2));
%o A378532 memoA378525 = Map();
%o A378532 A378525(n) = if(1==n,1,my(v); if(mapisdefined(memoA378525,n,&v), v, v = -sumdiv(n,d,if(d<n,A378542(n/d)*A378525(d),0)); mapput(memoA378525,n,v); (v)));
%o A378532 A378532(n) = sumdiv(n,d,A296075(d)*A378525(n/d));
%Y A378532 Cf. A033879, A296075, A378531 (Dirichlet inverse), A378534 (Möbius transform), A378525, A378542.
%Y A378532 Cf. also A378218.
%K A378532 sign
%O A378532 1,4
%A A378532 _Antti Karttunen_, Dec 01 2024