cp's OEIS Frontend

A378533 Dirichlet convolution of A323910 and A378542.

%I A378533 #9 Dec 01 2024 13:41:16
%S A378533 1,1,1,3,1,4,1,5,3,4,1,10,1,4,4,11,1,10,1,10,4,4,1,26,3,4,5,10,1,16,1,
%T A378533 21,4,4,4,34,1,4,4,26,1,16,1,10,10,4,1,62,3,10,4,10,1,26,4,26,4,4,1,
%U A378533 56,1,4,10,43,4,16,1,10,4,16,1,98,1,4,10,10,4,16,1,62,11,4,1,56,4,4,4,26,1,56,4,10,4,4,4
%N A378533 Dirichlet convolution of A323910 and A378542.
%C A378533 Inverse Möbius transform of A378531.
%H A378533 Antti Karttunen, <a href="/A378533/b378533.txt">Table of n, a(n) for n = 1..20000</a>
%F A378533 a(n) = Sum_{d|n} A323910(d)*A378542(n/d).
%F A378533 a(n) = Sum_{d|n} A378531(d).
%o A378533 (PARI)
%o A378533 A378542(n) = sumdiv(n,d,d*!(bigomega(n/d)%2));
%o A378533 A033879(n) = (n+n-sigma(n));
%o A378533 memoA323910 = Map();
%o A378533 A323910(n) = if(1==n,1,my(v); if(mapisdefined(memoA323910,n,&v), v, v = -sumdiv(n,d,if(d<n,A033879(n/d)*A323910(d),0)); mapput(memoA323910,n,v); (v)));
%o A378533 A378533(n) = sumdiv(n,d,A323910(d)*A378542(n/d));
%Y A378533 Cf. A323910, A378542.
%Y A378533 Cf. A378531 (Möbius transform), A378534 (Dirichlet inverse).
%Y A378533 Cf. also A378223.
%K A378533 nonn
%O A378533 1,4
%A A378533 _Antti Karttunen_, Dec 01 2024