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A304526 Möbius transform of A064664, the inverse of EKG-sequence.

%I A304526 #10 Jan 27 2024 17:06:05
%S A304526 1,1,4,1,9,-2,13,5,1,-2,19,2,27,-2,-3,9,32,7,36,8,-3,-2,42,4,14,-2,16,
%T A304526 12,56,15,60,14,-3,-2,2,15,66,-2,-3,17,73,23,80,21,27,-2,88,20,36,23,
%U A304526 -3,19,99,20,24,18,-3,-2,106,18,114,-2,35,33,17,41,127,32,-3,33,133,24,137,-2,44,34,45,44,150,23,54,-2,159,27,42,-2,-3,33,166,25,52
%N A304526 Möbius transform of A064664, the inverse of EKG-sequence.
%H A304526 Antti Karttunen, <a href="/A304526/b304526.txt">Table of n, a(n) for n = 1..32768</a>
%H A304526 <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>
%F A304526 a(n) = Sum_{d|n} A008683(n/d)*A064664(d).
%F A304526 a(n) = A064664(n) - A304527(n).
%F A304526 For all n >= 1, a(A000040(n)) = A064423(n).
%F A304526 For n >= 2, a(2*A000040(n)) = -2.
%F A304526 For n >= 3, a(3*A000040(n)) = -3.
%F A304526 a(n) = Sum_{d|n} A000010(n/d)*A349617(d). - _Antti Karttunen_, Jan 27 2024
%o A304526 (PARI) A304526(n) = sumdiv(n, d, moebius(n/d)*A064664(d));
%Y A304526 Cf. A000010, A008683, A064423, A064664, A304527, A327867 (even bisection), A323411, A349617.
%K A304526 sign
%O A304526 1,3
%A A304526 _Antti Karttunen_, May 18 2018