A378224 - OEIS

%I #8 Nov 25 2024 16:34:57

%S 1,-1,-2,-1,-2,0,-2,-1,0,0,-2,0,-2,0,2,-1,-2,0,-2,0,2,0,-2,0,0,0,0,0,

%T -2,0,-2,-1,2,0,2,0,-2,0,2,0,-2,0,-2,0,0,0,-2,0,0,0,2,0,-2,0,2,0,2,0,

%U -2,0,-2,0,0,-1,2,0,-2,0,2,0,-2,0,-2,0,0,0,2,0,-2,0,0,0,-2,0,2,0,2,0,-2,0,2,0,2,0,2,0,-2

%N Dirichlet inverse of A378223.

%C Möbius transform of A378218.

%H Antti Karttunen, <a href="/A378224/b378224.txt">Table of n, a(n) for n = 1..65537</a>

%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A378223(n/d) * a(d).

%F a(n) = Sum_{d|n} A008683(n/d)*A378218(d).

%o (PARI)

%o memoA345182 = Map();

%o A345182(n) = if(n<=2, n%2, my(v); if(mapisdefined(memoA345182,n,&v), v, v = sumdiv(n,d,if(d<n,A345182(d),0)); mapput(memoA345182,n,v); (v)));

%o A378223(n) = sumdiv(n,d,A345182(d));

%o memoA378224 = Map();

%o A378224(n) = if(1==n,1,my(v); if(mapisdefined(memoA378224,n,&v), v, v = -sumdiv(n,d,if(d<n,A378223(n/d)*A378224(d),0)); mapput(memoA378224,n,v); (v)));

%Y Cf. A008683, A345182, A378218, A378223.

%Y Cf. also A378225.

%K sign

%O 1,3

%A _Antti Karttunen_, Nov 25 2024