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A378440 Dirichlet inverse of Möbius transform of A033630, where A033630 is the number of partitions of n into distinct divisors of n.

%I A378440 #8 Nov 27 2024 15:56:47
%S A378440 1,0,0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,-1,0,-1,0,0,0,-3,0,0,0,-1,0,-2,0,
%T A378440 0,0,0,0,-3,0,0,0,-2,0,-1,0,0,0,0,0,-5,0,0,0,0,0,-1,0,-1,0,0,0,-29,0,
%U A378440 0,0,0,0,-1,0,0,0,0,0,-19,0,0,0,0,0,0,0,-3,0,0,0,-21,0,0,0,-1,0,-19,0,0,0,0,0,-11,0,0,0,-1
%N A378440 Dirichlet inverse of Möbius transform of A033630, where A033630 is the number of partitions of n into distinct divisors of n.
%C A378440 Equally, inverse Möbius transform of A378437, which is the Dirichlet inverse of A033630.
%H A378440 Antti Karttunen, <a href="/A378440/b378440.txt">Table of n, a(n) for n = 1..20000</a>
%F A378440 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A378439(n/d) * a(d).
%F A378440 a(n) = Sum_{d|n} A378437(d).
%o A378440 (PARI)
%o A378440 A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
%o A378440 A378439(n) = sumdiv(n, d, moebius(n/d)*A033630(d));
%o A378440 memoA378440 = Map();
%o A378440 A378440(n) = if(1==n,1,my(v); if(mapisdefined(memoA378440,n,&v), v, v = -sumdiv(n,d,if(d<n,A378439(n/d)*A378440(d),0)); mapput(memoA378440,n,v); (v)));
%Y A378440 Inverse Möbius transform of A378437.
%Y A378440 Dirichlet inverse of A378439.
%Y A378440 Cf. A033630.
%K A378440 sign
%O A378440 1,24
%A A378440 _Antti Karttunen_, Nov 27 2024