A378533 - OEIS

%I #9 Dec 01 2024 13:41:16

%S 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 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 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 Dirichlet convolution of A323910 and A378542.

%C Inverse Möbius transform of A378531.

%H Antti Karttunen, <a href="/A378533/b378533.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = Sum_{d|n} A323910(d)*A378542(n/d).

%F a(n) = Sum_{d|n} A378531(d).

%o (PARI)

%o A378542(n) = sumdiv(n,d,d*!(bigomega(n/d)%2));

%o A033879(n) = (n+n-sigma(n));

%o memoA323910 = Map();

%o 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(n) = sumdiv(n,d,A323910(d)*A378542(n/d));

%Y Cf. A323910, A378542.

%Y Cf. A378531 (Möbius transform), A378534 (Dirichlet inverse).

%Y Cf. also A378223.

%K nonn

%O 1,4

%A _Antti Karttunen_, Dec 01 2024