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A378446 Inverse Möbius transform of A083206, where A083206(n) is the number of ways of partitioning the divisors of n into two disjoint sets with equal sum.

%I A378446 #6 Nov 28 2024 10:49:58
%S A378446 0,0,0,0,0,1,0,0,0,0,0,2,0,0,0,0,0,1,0,1,0,0,0,5,0,0,0,1,0,4,0,0,0,0,
%T A378446 0,2,0,0,0,3,0,3,0,0,0,0,0,10,0,0,0,0,0,3,0,2,0,0,0,23,0,0,0,0,0,3,0,
%U A378446 0,0,1,0,5,0,0,0,0,0,3,0,6,0,0,0,19,0,0,0,1,0,17,0,0,0,0,0,21,0,0,0,1,0,3,0,1,0,0,0,12
%N A378446 Inverse Möbius transform of A083206, where A083206(n) is the number of ways of partitioning the divisors of n into two disjoint sets with equal sum.
%H A378446 Antti Karttunen, <a href="/A378446/b378446.txt">Table of n, a(n) for n = 1..20000</a>
%F A378446 a(n) = Sum_{d|n} A083206(d).
%o A378446 (PARI)
%o A378446 A083206(n) = { my(p=1); fordiv(n, d, p *= ('x^d + 'x^-d)); (polcoeff(p, 0)/2); };
%o A378446 A378446(n) = sumdiv(n,d,A083206(d));
%Y A378446 Cf. A083206.
%K A378446 nonn
%O A378446 1,12
%A A378446 _Antti Karttunen_, Nov 28 2024