A378536 - OEIS

%I #8 Dec 01 2024 19:54:30

%S 1,-1,-2,-2,-4,1,-6,0,-3,3,-10,5,-12,5,7,0,-16,5,-18,9,11,9,-22,2,-5,

%T 11,0,13,-28,-1,-30,0,19,15,23,5,-36,17,23,2,-40,-3,-42,21,14,21,-46,

%U 0,-7,9,31,25,-52,3,39,2,35,27,-58,-18,-60,29,20,0,47,-7,-66,33,43,-13,-70,-5,-72,35,14,37,59,-9,-78,0,0

%N Inverse Möbius transform of A378525.

%C Dirichlet inverse of A378535, which is Möbius transform of A378542, where A378542 is the sum of divisors d of n such that n/d has an even number of prime factors (counted with multiplicity).

%H Antti Karttunen, <a href="/A378536/b378536.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = Sum_{d|n} A378525(d).

%o (PARI)

%o memoA378525 = Map();

%o 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 A378536(n) = sumdiv(n,d,A378525(d));

%Y Cf. A378525, A378535 (Dirichlet inverse), A378542.

%K sign

%O 1,3

%A _Antti Karttunen_, Dec 01 2024