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A378525 Dirichlet inverse 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).

%I A378525 #7 Dec 01 2024 10:05:27
%S A378525 1,-2,-3,-1,-5,5,-7,2,-1,9,-11,5,-13,13,14,0,-17,5,-19,7,20,21,-23,-5,
%T A378525 -1,25,3,9,-29,-20,-31,0,32,33,34,-4,-37,37,38,-9,-41,-30,-43,13,8,45,
%U A378525 -47,-2,-1,7,50,15,-53,-5,54,-13,56,57,-59,-28,-61,61,10,0,64,-50,-67,19,68,-56,-71,-7,-73,73,8,21,76
%N A378525 Dirichlet inverse 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 A378525 Antti Karttunen, <a href="/A378525/b378525.txt">Table of n, a(n) for n = 1..20000</a>
%F A378525 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A378542(n/d) * a(d).
%o A378525 (PARI)
%o A378525 A378542(n) = sumdiv(n,d,d*!(bigomega(n/d)%2));
%o A378525 memoA378525 = Map();
%o A378525 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)));
%Y A378525 Cf. A378542.
%Y A378525 Cf. also A378526.
%K A378525 sign
%O A378525 1,2
%A A378525 _Antti Karttunen_, Dec 01 2024