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A378451 Dirichlet inverse of A119347, where A119347(n) is the number of distinct sums of distinct divisors of n.

%I A378451 #6 Nov 29 2024 15:09:34
%S A378451 1,-3,-3,2,-3,6,-3,0,2,3,-3,5,-3,3,3,0,-3,-6,-3,9,3,3,-3,-12,2,3,0,-5,
%T A378451 -3,18,-3,0,3,3,3,13,-3,3,3,3,-3,-6,-3,-12,-4,3,-3,4,2,-12,3,-12,-3,
%U A378451 -6,3,57,3,3,-3,-15,-3,3,-8,0,3,-54,-3,-12,3,-34,-3,-39,-3,3,-12,-12,3,-78,-3,-24,0,3,-3,157,3,3,3
%N A378451 Dirichlet inverse of A119347, where A119347(n) is the number of distinct sums of distinct divisors of n.
%H A378451 Antti Karttunen, <a href="/A378451/b378451.txt">Table of n, a(n) for n = 1..20000</a>
%F A378451 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A119347(n/d) * a(d).
%o A378451 (PARI)
%o A378451 A119347(n) = { my(c=[0]); fordiv(n,d, c = Set(concat(c,vector(#c,i,c[i]+d)))); (#c)-1; };
%o A378451 memoA378451 = Map();
%o A378451 A378451(n) = if(1==n,1,my(v); if(mapisdefined(memoA378451,n,&v), v, v = -sumdiv(n,d,if(d<n,A119347(n/d)*A378451(d),0)); mapput(memoA378451,n,v); (v)));
%Y A378451 Cf. A119347.
%K A378451 sign
%O A378451 1,2
%A A378451 _Antti Karttunen_, Nov 29 2024