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A378439 Möbius transform of A033630, where A033630 is the number of partitions of n into distinct divisors of n.

%I A378439 #6 Nov 27 2024 15:56:43
%S A378439 1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,3,0,0,0,1,0,2,0,0,0,0,
%T A378439 0,4,0,0,0,2,0,1,0,0,0,0,0,5,0,0,0,0,0,1,0,1,0,0,0,29,0,0,0,0,0,1,0,0,
%U A378439 0,0,0,21,0,0,0,0,0,0,0,3,0,0,0,21,0,0,0,1,0,19,0,0,0,0,0,11,0,0,0,1,0,0,0,1,0,0,0,12
%N A378439 Möbius transform of A033630, where A033630 is the number of partitions of n into distinct divisors of n.
%H A378439 Antti Karttunen, <a href="/A378439/b378439.txt">Table of n, a(n) for n = 1..20000</a>
%F A378439 a(n) = Sum_{d|n} A008683(n/d)*A033630(d).
%o A378439 (PARI)
%o A378439 A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
%o A378439 A378439(n) = sumdiv(n, d, moebius(n/d)*A033630(d));
%Y A378439 Cf. A008683, A033630, A378440 (Dirichlet inverse).
%K A378439 nonn
%O A378439 1,24
%A A378439 _Antti Karttunen_, Nov 27 2024