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A324397 a(1) = 0; for n > 1, a(n) = A297114(A156552(n)).

%I A324397 #13 Mar 15 2019 12:35:42
%S A324397 0,0,0,0,0,2,0,3,-2,3,0,7,0,14,-2,0,0,9,0,15,-6,9,0,18,-4,33,-2,14,0,
%T A324397 4,0,25,-2,42,-4,7,0,254,-26,9,0,33,0,63,-2,140,0,41,-8,14,-34,127,0,
%U A324397 24,-12,66,-90,579,0,38,0,684,-2,6,-4,21,0,175,-2,37,0,24,0,3587,-2,304,-8,85,0,73,-14,2733,0,6,-52,8707,-378,11,0,3
%N A324397 a(1) = 0; for n > 1, a(n) = A297114(A156552(n)).
%H A324397 Antti Karttunen, <a href="/A324397/b324397.txt">Table of n, a(n) for n = 1..4137</a>
%F A324397 a(1) = 0; for n > 1, a(n) = A297114(A156552(n)).
%F A324397 For all n >= 1, a(2n-1) = A324103(2n-1).
%t A324397 Array[If[# == 1, 0, Function[n, DivisorSum[n, MoebiusMu[n/#] (2 # - DigitCount[2 #, 2, 1] - DivisorSigma[1, #]) &]]@ Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ #]]] &, 90] (* _Michael De Vlieger_, Mar 11 2019 *)
%o A324397 (PARI)
%o A324397 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A324397 A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
%o A324397 A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
%o A324397 \\ Slow: A297114(n) = sumdiv(n,d,moebius(n/d)*(A005187(d)-sigma(d)));
%o A324397 A297111(n) = sumdiv(n,d,moebius(n/d)*A005187(d));
%o A324397 A297114(n) = (A297111(n) - n);
%o A324397 A324397(n) = if(1==n,0,A297114(A156552(n)));
%Y A324397 Cf. A000203, A005187, A156552, A297114, A323243, A323244, A324103, A323247, A323248, A324396, A324398, A324542.
%K A324397 sign
%O A324397 1,6
%A A324397 _Antti Karttunen_, Mar 05 2019