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A378596 Möbius transform of A119347, where A119347 number of distinct sums of nonempty subsets of divisors of n.

%I A378596 #7 Dec 02 2024 15:39:55
%S A378596 1,2,2,4,2,7,2,8,4,10,2,12,2,10,10,16,2,23,2,23,10,10,2,24,4,10,8,37,
%T A378596 2,38,2,32,10,10,10,36,2,10,10,40,2,62,2,44,36,10,2,48,4,44,10,44,2,
%U A378596 73,10,56,10,10,2,57,2,10,40,64,10,110,2,44,10,105,2,72,2,10,44,44,10,134,2,80,16,10,2,75,10,10,10
%N A378596 Möbius transform of A119347, where A119347 number of distinct sums of nonempty subsets of divisors of n.
%H A378596 Antti Karttunen, <a href="/A378596/b378596.txt">Table of n, a(n) for n = 1..20000</a>
%F A378596 a(n) = Sum_{d|n} A008683(d)*A119347(n/d).
%F A378596 a(n) = n - A378597(n).
%o A378596 (PARI)
%o A378596 A119347(n) = { my(c=[0]); fordiv(n,d, c = Set(concat(c,vector(#c,i,c[i]+d)))); (#c)-1; };
%o A378596 A378596(n) = sumdiv(n,d,moebius(n/d)*A119347(d));
%Y A378596 Cf. A008683, A119347, A378597.
%K A378596 nonn
%O A378596 1,2
%A A378596 _Antti Karttunen_, Dec 02 2024